KILLED proof of input_dloCFqR257.trs # AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 51 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) RenamingProof [BOTH BOUNDS(ID, ID), 4 ms] (12) CpxRelTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 31 ms] (16) typed CpxTrs (17) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (18) CpxWeightedTrs (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedTrs (21) CompletionProof [UPPER BOUND(ID), 0 ms] (22) CpxTypedWeightedCompleteTrs (23) NarrowingProof [BOTH BOUNDS(ID, ID), 687 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) InliningProof [UPPER BOUND(ID), 852 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxRelTRS (43) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (44) CpxTRS (45) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxWeightedTrs (47) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxTypedWeightedTrs (49) CompletionProof [UPPER BOUND(ID), 0 ms] (50) CpxTypedWeightedCompleteTrs (51) NarrowingProof [BOTH BOUNDS(ID, ID), 8153 ms] (52) CpxTypedWeightedCompleteTrs (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 19 ms] (54) CpxRNTS (55) InliningProof [UPPER BOUND(ID), 1736 ms] (56) CpxRNTS (57) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CpxRNTS (59) CompletionProof [UPPER BOUND(ID), 331 ms] (60) CpxTypedWeightedCompleteTrs (61) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms] (150) CdtProblem (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 73 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 179 ms] (162) CdtProblem (163) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 198 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 69 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 87 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 92 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 85 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 65 ms] (232) CdtProblem (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (234) CdtProblem (235) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms] (236) CdtProblem (237) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 17 ms] (238) CdtProblem (239) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 64 ms] (240) CdtProblem (241) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (242) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt) -> tt a__U21(tt) -> tt a__U31(tt) -> tt a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) a__U42(tt) -> tt a__U51(tt, V2) -> a__U52(a__isNatList(V2)) a__U52(tt) -> tt a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) a__U62(tt) -> tt a__U71(tt, L, N) -> a__U72(a__isNat(N), L) a__U72(tt, L) -> s(a__length(mark(L))) a__U81(tt) -> nil a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__isNat(0) -> tt a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNatIList(V) -> a__U31(a__isNatList(V)) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) a__take(0, IL) -> a__U81(a__isNatIList(IL)) a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) mark(zeros) -> a__zeros mark(U11(X)) -> a__U11(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1, X2)) -> a__U41(mark(X1), X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1, X2)) -> a__U51(mark(X1), X2) mark(U52(X)) -> a__U52(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U61(X1, X2)) -> a__U61(mark(X1), X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) mark(U72(X1, X2)) -> a__U72(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(length(X)) -> a__length(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X) -> U11(X) a__U21(X) -> U21(X) a__U31(X) -> U31(X) a__U41(X1, X2) -> U41(X1, X2) a__U42(X) -> U42(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1, X2) -> U51(X1, X2) a__U52(X) -> U52(X) a__isNatList(X) -> isNatList(X) a__U61(X1, X2) -> U61(X1, X2) a__U62(X) -> U62(X) a__U71(X1, X2, X3) -> U71(X1, X2, X3) a__U72(X1, X2) -> U72(X1, X2) a__isNat(X) -> isNat(X) a__length(X) -> length(X) a__U81(X) -> U81(X) a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) a__take(X1, X2) -> take(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0', zeros) a__U11(tt) -> tt a__U21(tt) -> tt a__U31(tt) -> tt a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) a__U42(tt) -> tt a__U51(tt, V2) -> a__U52(a__isNatList(V2)) a__U52(tt) -> tt a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) a__U62(tt) -> tt a__U71(tt, L, N) -> a__U72(a__isNat(N), L) a__U72(tt, L) -> s(a__length(mark(L))) a__U81(tt) -> nil a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__isNat(0') -> tt a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNatIList(V) -> a__U31(a__isNatList(V)) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) a__length(nil) -> 0' a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) a__take(0', IL) -> a__U81(a__isNatIList(IL)) a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) mark(zeros) -> a__zeros mark(U11(X)) -> a__U11(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1, X2)) -> a__U41(mark(X1), X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1, X2)) -> a__U51(mark(X1), X2) mark(U52(X)) -> a__U52(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U61(X1, X2)) -> a__U61(mark(X1), X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) mark(U72(X1, X2)) -> a__U72(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(length(X)) -> a__length(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0') -> 0' mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X) -> U11(X) a__U21(X) -> U21(X) a__U31(X) -> U31(X) a__U41(X1, X2) -> U41(X1, X2) a__U42(X) -> U42(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1, X2) -> U51(X1, X2) a__U52(X) -> U52(X) a__isNatList(X) -> isNatList(X) a__U61(X1, X2) -> U61(X1, X2) a__U62(X) -> U62(X) a__U71(X1, X2, X3) -> U71(X1, X2, X3) a__U72(X1, X2) -> U72(X1, X2) a__isNat(X) -> isNat(X) a__length(X) -> length(X) a__U81(X) -> U81(X) a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) a__take(X1, X2) -> take(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt) -> tt a__U21(tt) -> tt a__U31(tt) -> tt a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) a__U42(tt) -> tt a__U51(tt, V2) -> a__U52(a__isNatList(V2)) a__U52(tt) -> tt a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) a__U62(tt) -> tt a__U71(tt, L, N) -> a__U72(a__isNat(N), L) a__U72(tt, L) -> s(a__length(mark(L))) a__U81(tt) -> nil a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__isNat(0) -> tt a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNatIList(V) -> a__U31(a__isNatList(V)) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) a__take(0, IL) -> a__U81(a__isNatIList(IL)) a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) mark(zeros) -> a__zeros mark(U11(X)) -> a__U11(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1, X2)) -> a__U41(mark(X1), X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1, X2)) -> a__U51(mark(X1), X2) mark(U52(X)) -> a__U52(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U61(X1, X2)) -> a__U61(mark(X1), X2) mark(U62(X)) -> a__U62(mark(X)) mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) mark(U72(X1, X2)) -> a__U72(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(length(X)) -> a__length(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X) -> U11(X) a__U21(X) -> U21(X) a__U31(X) -> U31(X) a__U41(X1, X2) -> U41(X1, X2) a__U42(X) -> U42(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1, X2) -> U51(X1, X2) a__U52(X) -> U52(X) a__isNatList(X) -> isNatList(X) a__U61(X1, X2) -> U61(X1, X2) a__U62(X) -> U62(X) a__U71(X1, X2, X3) -> U71(X1, X2, X3) a__U72(X1, X2) -> U72(X1, X2) a__isNat(X) -> isNat(X) a__length(X) -> length(X) a__U81(X) -> U81(X) a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) a__take(X1, X2) -> take(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0) -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0) -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 S tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0) -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0) -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__U11_1, A__U21_1, A__U31_1, A__U41_2, A__U42_1, A__U51_2, A__U52_1, A__U61_2, A__U62_1, A__U71_3, A__U72_2, A__U81_1, A__U91_4, A__U92_4, A__U93_4, A__ISNAT_1, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8_2, c9, c10, c11, c12_2, c13, c14, c15, c16_2, c17, c18, c19, c20_2, c21, c22_2, c23, c24, c25, c26_2, c27, c28_2, c29, c30_1, c31, c32, c33_2, c34_2, c35, c36_2, c37, c38_2, c39, c40, c41_2, c42_2, c43, c44, c45_2, c46, c47_2, c48_2, c49, c50_1, c51_2, c52_2, c53_2, c54_2, c55_2, c56_1, c57_2, c58_2, c59_1, c60_2, c61_2, c62_2, c63_2, c64_1, c65_2, c66_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c73, c74, c75_1, c76 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0) -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0) -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (10) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0) -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0) -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (11) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (12) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0') -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0', z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0') -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 The (relative) TRS S consists of the following rules: a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0') -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0', z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (13) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0') -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0', z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0') -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0') -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0', z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c2:c3 tt :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c2 :: c2:c3 c3 :: c2:c3 A__U21 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c4:c5 c4 :: c4:c5 c5 :: c4:c5 A__U31 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c6:c7 c6 :: c6:c7 c7 :: c6:c7 A__U41 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c8:c9 c8 :: c10:c11 -> c36:c37:c38:c39 -> c8:c9 A__U42 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c10:c11 a__isNatIList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 A__ISNATILIST :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c36:c37:c38:c39 c9 :: c8:c9 c10 :: c10:c11 c11 :: c10:c11 A__U51 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c12:c13 c12 :: c14:c15 -> c40:c41:c42:c43 -> c12:c13 A__U52 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c14:c15 a__isNatList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 A__ISNATLIST :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c40:c41:c42:c43 c13 :: c12:c13 c14 :: c14:c15 c15 :: c14:c15 A__U61 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c16:c17 c16 :: c18:c19 -> c36:c37:c38:c39 -> c16:c17 A__U62 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c18:c19 c17 :: c16:c17 c18 :: c18:c19 c19 :: c18:c19 A__U71 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c20:c21 c20 :: c22:c23 -> c32:c33:c34:c35 -> c20:c21 A__U72 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c22:c23 a__isNat :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 A__ISNAT :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c32:c33:c34:c35 c21 :: c20:c21 c22 :: c44:c45:c46 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c22:c23 A__LENGTH :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c44:c45:c46 mark :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 MARK :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c23 :: c22:c23 A__U81 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c24:c25 c24 :: c24:c25 c25 :: c24:c25 A__U91 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c26:c27 c26 :: c28:c29 -> c32:c33:c34:c35 -> c26:c27 A__U92 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c28:c29 c27 :: c26:c27 c28 :: c30:c31 -> c32:c33:c34:c35 -> c28:c29 A__U93 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c30:c31 c29 :: c28:c29 c30 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c30:c31 c31 :: c30:c31 0' :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c32 :: c32:c33:c34:c35 length :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c33 :: c2:c3 -> c40:c41:c42:c43 -> c32:c33:c34:c35 s :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c34 :: c4:c5 -> c32:c33:c34:c35 -> c32:c33:c34:c35 c35 :: c32:c33:c34:c35 c36 :: c6:c7 -> c40:c41:c42:c43 -> c36:c37:c38:c39 zeros :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c37 :: c36:c37:c38:c39 cons :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c38 :: c8:c9 -> c32:c33:c34:c35 -> c36:c37:c38:c39 c39 :: c36:c37:c38:c39 nil :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c40 :: c40:c41:c42:c43 c41 :: c12:c13 -> c32:c33:c34:c35 -> c40:c41:c42:c43 take :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c42 :: c16:c17 -> c32:c33:c34:c35 -> c40:c41:c42:c43 c43 :: c40:c41:c42:c43 c44 :: c44:c45:c46 c45 :: c20:c21 -> c40:c41:c42:c43 -> c44:c45:c46 c46 :: c44:c45:c46 A__TAKE :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c47:c48:c49 c47 :: c24:c25 -> c36:c37:c38:c39 -> c47:c48:c49 c48 :: c26:c27 -> c36:c37:c38:c39 -> c47:c48:c49 c49 :: c47:c48:c49 c50 :: c:c1 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U11 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c51 :: c2:c3 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U21 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c52 :: c4:c5 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U31 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c53 :: c6:c7 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U41 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c54 :: c8:c9 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U42 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c55 :: c10:c11 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 isNatIList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c56 :: c36:c37:c38:c39 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U51 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c57 :: c12:c13 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U52 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c58 :: c14:c15 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 isNatList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c59 :: c40:c41:c42:c43 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U61 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c60 :: c16:c17 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U62 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c61 :: c18:c19 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U71 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c62 :: c20:c21 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U72 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c63 :: c22:c23 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 isNat :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c64 :: c32:c33:c34:c35 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c65 :: c44:c45:c46 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U81 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c66 :: c24:c25 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U91 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c67 :: c26:c27 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U92 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c68 :: c28:c29 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U93 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c69 :: c30:c31 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c70 :: c47:c48:c49 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c71 :: c47:c48:c49 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c72 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c73 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c74 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c75 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c76 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 a__zeros :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U11 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U21 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U31 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U41 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U42 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U51 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U52 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U61 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U62 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U71 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U72 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__length :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U81 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U91 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U92 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U93 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__take :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 hole_c:c11_77 :: c:c1 hole_c2:c32_77 :: c2:c3 hole_tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U933_77 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 hole_c4:c54_77 :: c4:c5 hole_c6:c75_77 :: c6:c7 hole_c8:c96_77 :: c8:c9 hole_c10:c117_77 :: c10:c11 hole_c36:c37:c38:c398_77 :: c36:c37:c38:c39 hole_c12:c139_77 :: c12:c13 hole_c14:c1510_77 :: c14:c15 hole_c40:c41:c42:c4311_77 :: c40:c41:c42:c43 hole_c16:c1712_77 :: c16:c17 hole_c18:c1913_77 :: c18:c19 hole_c20:c2114_77 :: c20:c21 hole_c22:c2315_77 :: c22:c23 hole_c32:c33:c34:c3516_77 :: c32:c33:c34:c35 hole_c44:c45:c4617_77 :: c44:c45:c46 hole_c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c7618_77 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 hole_c24:c2519_77 :: c24:c25 hole_c26:c2720_77 :: c26:c27 hole_c28:c2921_77 :: c28:c29 hole_c30:c3122_77 :: c30:c31 hole_c47:c48:c4923_77 :: c47:c48:c49 gen_tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U9324_77 :: Nat -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 gen_c32:c33:c34:c3525_77 :: Nat -> c32:c33:c34:c35 gen_c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c7626_77 :: Nat -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 ---------------------------------------- (15) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U41, a__isNatIList, A__ISNATILIST, A__U51, a__isNatList, A__ISNATLIST, A__U61, A__U71, A__U72, a__isNat, A__ISNAT, A__LENGTH, mark, MARK, A__U91, A__U92, A__U93, a__U41, a__U51, a__U61, a__U71, a__U72, a__length, a__U91, a__U92, a__U93 They will be analysed ascendingly in the following order: a__isNatIList < A__U41 A__U41 = A__ISNATILIST A__U41 = A__U51 A__U41 = A__ISNATLIST A__U41 = A__U61 A__U41 = A__ISNAT A__U41 < MARK a__isNatIList = a__isNatList a__isNatIList < A__U61 a__isNatIList = a__isNat a__isNatIList < mark a__isNatIList < MARK a__isNatIList = a__U41 a__isNatIList = a__U51 a__isNatIList = a__U61 A__ISNATILIST = A__U51 a__isNatList < A__ISNATILIST A__ISNATILIST = A__ISNATLIST A__ISNATILIST = A__U61 a__isNat < A__ISNATILIST A__ISNATILIST = A__ISNAT A__ISNATILIST < MARK a__isNatList < A__U51 A__U51 = A__ISNATLIST A__U51 = A__U61 A__U51 = A__ISNAT A__U51 < MARK a__isNatList = a__isNat a__isNatList < A__ISNAT a__isNatList < A__LENGTH a__isNatList < mark a__isNatList = a__U41 a__isNatList = a__U51 a__isNatList = a__U61 a__isNatList < a__length A__ISNATLIST = A__U61 a__isNat < A__ISNATLIST A__ISNATLIST = A__ISNAT A__ISNATLIST < A__LENGTH A__ISNATLIST < MARK A__U61 = A__ISNAT A__U61 < MARK A__U71 = A__U72 a__isNat < A__U71 A__ISNAT < A__U71 A__U71 = A__LENGTH A__U71 = MARK A__U71 = A__U91 A__U71 = A__U92 A__U71 = A__U93 A__U72 = A__LENGTH mark < A__U72 A__U72 = MARK A__U72 = A__U91 A__U72 = A__U92 A__U72 = A__U93 a__isNat < A__ISNAT a__isNat < mark a__isNat < A__U91 a__isNat < A__U92 a__isNat = a__U41 a__isNat = a__U51 a__isNat = a__U61 a__isNat < a__U71 a__isNat < a__U91 a__isNat < a__U92 A__ISNAT < MARK A__ISNAT < A__U91 A__ISNAT < A__U92 A__LENGTH = MARK A__LENGTH = A__U91 A__LENGTH = A__U92 A__LENGTH = A__U93 mark < MARK a__U41 < mark a__U51 < mark a__U61 < mark mark = a__U71 mark = a__U72 mark = a__length mark = a__U91 mark = a__U92 mark = a__U93 MARK = A__U91 MARK = A__U92 MARK = A__U93 A__U91 = A__U92 A__U91 = A__U93 A__U92 = A__U93 a__U41 = a__U51 a__U41 = a__U61 a__U51 = a__U61 a__U71 = a__U72 a__U71 = a__length a__U71 = a__U91 a__U71 = a__U92 a__U71 = a__U93 a__U72 = a__length a__U72 = a__U91 a__U72 = a__U92 a__U72 = a__U93 a__length = a__U91 a__length = a__U92 a__length = a__U93 a__U91 = a__U92 a__U91 = a__U93 a__U92 = a__U93 ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0') -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0', z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0') -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0') -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0', z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c2:c3 tt :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c2 :: c2:c3 c3 :: c2:c3 A__U21 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c4:c5 c4 :: c4:c5 c5 :: c4:c5 A__U31 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c6:c7 c6 :: c6:c7 c7 :: c6:c7 A__U41 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c8:c9 c8 :: c10:c11 -> c36:c37:c38:c39 -> c8:c9 A__U42 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c10:c11 a__isNatIList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 A__ISNATILIST :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c36:c37:c38:c39 c9 :: c8:c9 c10 :: c10:c11 c11 :: c10:c11 A__U51 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c12:c13 c12 :: c14:c15 -> c40:c41:c42:c43 -> c12:c13 A__U52 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c14:c15 a__isNatList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 A__ISNATLIST :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c40:c41:c42:c43 c13 :: c12:c13 c14 :: c14:c15 c15 :: c14:c15 A__U61 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c16:c17 c16 :: c18:c19 -> c36:c37:c38:c39 -> c16:c17 A__U62 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c18:c19 c17 :: c16:c17 c18 :: c18:c19 c19 :: c18:c19 A__U71 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c20:c21 c20 :: c22:c23 -> c32:c33:c34:c35 -> c20:c21 A__U72 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c22:c23 a__isNat :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 A__ISNAT :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c32:c33:c34:c35 c21 :: c20:c21 c22 :: c44:c45:c46 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c22:c23 A__LENGTH :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c44:c45:c46 mark :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 MARK :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c23 :: c22:c23 A__U81 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c24:c25 c24 :: c24:c25 c25 :: c24:c25 A__U91 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c26:c27 c26 :: c28:c29 -> c32:c33:c34:c35 -> c26:c27 A__U92 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c28:c29 c27 :: c26:c27 c28 :: c30:c31 -> c32:c33:c34:c35 -> c28:c29 A__U93 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c30:c31 c29 :: c28:c29 c30 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c30:c31 c31 :: c30:c31 0' :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c32 :: c32:c33:c34:c35 length :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c33 :: c2:c3 -> c40:c41:c42:c43 -> c32:c33:c34:c35 s :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c34 :: c4:c5 -> c32:c33:c34:c35 -> c32:c33:c34:c35 c35 :: c32:c33:c34:c35 c36 :: c6:c7 -> c40:c41:c42:c43 -> c36:c37:c38:c39 zeros :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c37 :: c36:c37:c38:c39 cons :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c38 :: c8:c9 -> c32:c33:c34:c35 -> c36:c37:c38:c39 c39 :: c36:c37:c38:c39 nil :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c40 :: c40:c41:c42:c43 c41 :: c12:c13 -> c32:c33:c34:c35 -> c40:c41:c42:c43 take :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c42 :: c16:c17 -> c32:c33:c34:c35 -> c40:c41:c42:c43 c43 :: c40:c41:c42:c43 c44 :: c44:c45:c46 c45 :: c20:c21 -> c40:c41:c42:c43 -> c44:c45:c46 c46 :: c44:c45:c46 A__TAKE :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> c47:c48:c49 c47 :: c24:c25 -> c36:c37:c38:c39 -> c47:c48:c49 c48 :: c26:c27 -> c36:c37:c38:c39 -> c47:c48:c49 c49 :: c47:c48:c49 c50 :: c:c1 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U11 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c51 :: c2:c3 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U21 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c52 :: c4:c5 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U31 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c53 :: c6:c7 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U41 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c54 :: c8:c9 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U42 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c55 :: c10:c11 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 isNatIList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c56 :: c36:c37:c38:c39 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U51 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c57 :: c12:c13 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U52 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c58 :: c14:c15 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 isNatList :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c59 :: c40:c41:c42:c43 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U61 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c60 :: c16:c17 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U62 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c61 :: c18:c19 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U71 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c62 :: c20:c21 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U72 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c63 :: c22:c23 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 isNat :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c64 :: c32:c33:c34:c35 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c65 :: c44:c45:c46 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U81 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c66 :: c24:c25 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U91 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c67 :: c26:c27 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U92 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c68 :: c28:c29 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 U93 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 c69 :: c30:c31 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c70 :: c47:c48:c49 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c71 :: c47:c48:c49 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c72 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c73 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c74 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c75 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 c76 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 a__zeros :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U11 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U21 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U31 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U41 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U42 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U51 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U52 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U61 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U62 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U71 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U72 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__length :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U81 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U91 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U92 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U93 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__take :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 hole_c:c11_77 :: c:c1 hole_c2:c32_77 :: c2:c3 hole_tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U933_77 :: tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 hole_c4:c54_77 :: c4:c5 hole_c6:c75_77 :: c6:c7 hole_c8:c96_77 :: c8:c9 hole_c10:c117_77 :: c10:c11 hole_c36:c37:c38:c398_77 :: c36:c37:c38:c39 hole_c12:c139_77 :: c12:c13 hole_c14:c1510_77 :: c14:c15 hole_c40:c41:c42:c4311_77 :: c40:c41:c42:c43 hole_c16:c1712_77 :: c16:c17 hole_c18:c1913_77 :: c18:c19 hole_c20:c2114_77 :: c20:c21 hole_c22:c2315_77 :: c22:c23 hole_c32:c33:c34:c3516_77 :: c32:c33:c34:c35 hole_c44:c45:c4617_77 :: c44:c45:c46 hole_c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c7618_77 :: c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 hole_c24:c2519_77 :: c24:c25 hole_c26:c2720_77 :: c26:c27 hole_c28:c2921_77 :: c28:c29 hole_c30:c3122_77 :: c30:c31 hole_c47:c48:c4923_77 :: c47:c48:c49 gen_tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U9324_77 :: Nat -> tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 gen_c32:c33:c34:c3525_77 :: Nat -> c32:c33:c34:c35 gen_c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c7626_77 :: Nat -> c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c76 Generator Equations: gen_tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U9324_77(0) <=> tt gen_tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U9324_77(+(x, 1)) <=> length(gen_tt:0':length:s:zeros:cons:nil:take:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U9324_77(x)) gen_c32:c33:c34:c3525_77(0) <=> c32 gen_c32:c33:c34:c3525_77(+(x, 1)) <=> c34(c4, gen_c32:c33:c34:c3525_77(x)) gen_c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c7626_77(0) <=> c50(c) gen_c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c7626_77(+(x, 1)) <=> c51(c2, gen_c50:c51:c52:c53:c54:c55:c56:c57:c58:c59:c60:c61:c62:c63:c64:c65:c66:c67:c68:c69:c70:c71:c72:c73:c74:c75:c7626_77(x)) The following defined symbols remain to be analysed: a__isNatList, A__U41, a__isNatIList, A__ISNATILIST, A__U51, A__ISNATLIST, A__U61, A__U71, A__U72, a__isNat, A__ISNAT, A__LENGTH, mark, MARK, A__U91, A__U92, A__U93, a__U41, a__U51, a__U61, a__U71, a__U72, a__length, a__U91, a__U92, a__U93 They will be analysed ascendingly in the following order: a__isNatIList < A__U41 A__U41 = A__ISNATILIST A__U41 = A__U51 A__U41 = A__ISNATLIST A__U41 = A__U61 A__U41 = A__ISNAT A__U41 < MARK a__isNatIList = a__isNatList a__isNatIList < A__U61 a__isNatIList = a__isNat a__isNatIList < mark a__isNatIList < MARK a__isNatIList = a__U41 a__isNatIList = a__U51 a__isNatIList = a__U61 A__ISNATILIST = A__U51 a__isNatList < A__ISNATILIST A__ISNATILIST = A__ISNATLIST A__ISNATILIST = A__U61 a__isNat < A__ISNATILIST A__ISNATILIST = A__ISNAT A__ISNATILIST < MARK a__isNatList < A__U51 A__U51 = A__ISNATLIST A__U51 = A__U61 A__U51 = A__ISNAT A__U51 < MARK a__isNatList = a__isNat a__isNatList < A__ISNAT a__isNatList < A__LENGTH a__isNatList < mark a__isNatList = a__U41 a__isNatList = a__U51 a__isNatList = a__U61 a__isNatList < a__length A__ISNATLIST = A__U61 a__isNat < A__ISNATLIST A__ISNATLIST = A__ISNAT A__ISNATLIST < A__LENGTH A__ISNATLIST < MARK A__U61 = A__ISNAT A__U61 < MARK A__U71 = A__U72 a__isNat < A__U71 A__ISNAT < A__U71 A__U71 = A__LENGTH A__U71 = MARK A__U71 = A__U91 A__U71 = A__U92 A__U71 = A__U93 A__U72 = A__LENGTH mark < A__U72 A__U72 = MARK A__U72 = A__U91 A__U72 = A__U92 A__U72 = A__U93 a__isNat < A__ISNAT a__isNat < mark a__isNat < A__U91 a__isNat < A__U92 a__isNat = a__U41 a__isNat = a__U51 a__isNat = a__U61 a__isNat < a__U71 a__isNat < a__U91 a__isNat < a__U92 A__ISNAT < MARK A__ISNAT < A__U91 A__ISNAT < A__U92 A__LENGTH = MARK A__LENGTH = A__U91 A__LENGTH = A__U92 A__LENGTH = A__U93 mark < MARK a__U41 < mark a__U51 < mark a__U61 < mark mark = a__U71 mark = a__U72 mark = a__length mark = a__U91 mark = a__U92 mark = a__U93 MARK = A__U91 MARK = A__U92 MARK = A__U93 A__U91 = A__U92 A__U91 = A__U93 A__U92 = A__U93 a__U41 = a__U51 a__U41 = a__U61 a__U51 = a__U61 a__U71 = a__U72 a__U71 = a__length a__U71 = a__U91 a__U71 = a__U92 a__U71 = a__U93 a__U72 = a__length a__U72 = a__U91 a__U72 = a__U92 a__U72 = a__U93 a__length = a__U91 a__length = a__U92 a__length = a__U93 a__U91 = a__U92 a__U91 = a__U93 a__U92 = a__U93 ---------------------------------------- (17) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt) -> tt [1] a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) [1] a__U42(tt) -> tt [1] a__U51(tt, V2) -> a__U52(a__isNatList(V2)) [1] a__U52(tt) -> tt [1] a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) [1] a__U62(tt) -> tt [1] a__U71(tt, L, N) -> a__U72(a__isNat(N), L) [1] a__U72(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) [1] a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) [1] a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNatIList(V) -> a__U31(a__isNatList(V)) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) [1] a__take(0, IL) -> a__U81(a__isNatIList(IL)) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X)) -> a__U11(mark(X)) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X)) -> a__U31(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U42(X)) -> a__U42(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X)) -> a__U52(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U61(X1, X2)) -> a__U61(mark(X1), X2) [1] mark(U62(X)) -> a__U62(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2)) -> a__U72(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) [1] mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X) -> U11(X) [1] a__U21(X) -> U21(X) [1] a__U31(X) -> U31(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U42(X) -> U42(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X) -> U52(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U61(X1, X2) -> U61(X1, X2) [1] a__U62(X) -> U62(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2) -> U72(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) [1] a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt) -> tt [1] a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) [1] a__U42(tt) -> tt [1] a__U51(tt, V2) -> a__U52(a__isNatList(V2)) [1] a__U52(tt) -> tt [1] a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) [1] a__U62(tt) -> tt [1] a__U71(tt, L, N) -> a__U72(a__isNat(N), L) [1] a__U72(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) [1] a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) [1] a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNatIList(V) -> a__U31(a__isNatList(V)) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) [1] a__take(0, IL) -> a__U81(a__isNatIList(IL)) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X)) -> a__U11(mark(X)) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X)) -> a__U31(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U42(X)) -> a__U42(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X)) -> a__U52(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U61(X1, X2)) -> a__U61(mark(X1), X2) [1] mark(U62(X)) -> a__U62(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2)) -> a__U72(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) [1] mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X) -> U11(X) [1] a__U21(X) -> U21(X) [1] a__U31(X) -> U31(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U42(X) -> U42(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X) -> U52(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U61(X1, X2) -> U61(X1, X2) [1] a__U62(X) -> U62(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2) -> U72(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) [1] a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 cons :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 0 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 tt :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U62 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U71 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U72 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNat :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 s :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__length :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 mark :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U81 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 nil :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U91 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U92 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U93 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 take :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 length :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__take :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U11 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U21 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U31 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U41 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U42 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNatIList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U51 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U52 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNatList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U61 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U62 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U71 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U72 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNat :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U81 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U91 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U92 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U93 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 Rewrite Strategy: INNERMOST ---------------------------------------- (21) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: a__isNatIList_1 mark_1 a__isNatList_1 a__isNat_1 a__U11_1 a__length_1 a__U52_1 a__U21_1 a__take_2 a__U71_3 a__zeros a__U41_2 a__U72_2 a__U81_1 a__U42_1 a__U92_4 a__U93_4 a__U61_2 a__U51_2 a__U91_4 a__U62_1 a__U31_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt) -> tt [1] a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) [1] a__U42(tt) -> tt [1] a__U51(tt, V2) -> a__U52(a__isNatList(V2)) [1] a__U52(tt) -> tt [1] a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) [1] a__U62(tt) -> tt [1] a__U71(tt, L, N) -> a__U72(a__isNat(N), L) [1] a__U72(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) [1] a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) [1] a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNatIList(V) -> a__U31(a__isNatList(V)) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) [1] a__take(0, IL) -> a__U81(a__isNatIList(IL)) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X)) -> a__U11(mark(X)) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X)) -> a__U31(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U42(X)) -> a__U42(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X)) -> a__U52(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U61(X1, X2)) -> a__U61(mark(X1), X2) [1] mark(U62(X)) -> a__U62(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2)) -> a__U72(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) [1] mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X) -> U11(X) [1] a__U21(X) -> U21(X) [1] a__U31(X) -> U31(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U42(X) -> U42(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X) -> U52(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U61(X1, X2) -> U61(X1, X2) [1] a__U62(X) -> U62(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2) -> U72(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) [1] a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 cons :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 0 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 tt :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 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0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U72 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNat :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U81 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U91 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U92 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U93 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 Rewrite Strategy: INNERMOST ---------------------------------------- (23) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt) -> tt [1] a__U41(tt, V2) -> a__U42(a__U31(a__isNatList(V2))) [2] a__U41(tt, zeros) -> a__U42(tt) [2] a__U41(tt, cons(V1', V2')) -> a__U42(a__U41(a__isNat(V1'), V2')) [2] a__U41(tt, V2) -> a__U42(isNatIList(V2)) [2] a__U42(tt) -> tt [1] a__U51(tt, nil) -> a__U52(tt) [2] a__U51(tt, cons(V1'', V2'')) -> a__U52(a__U51(a__isNat(V1''), V2'')) [2] a__U51(tt, take(V11, V21)) -> a__U52(a__U61(a__isNat(V11), V21)) [2] a__U51(tt, V2) -> a__U52(isNatList(V2)) [2] a__U52(tt) -> tt [1] a__U61(tt, V2) -> a__U62(a__U31(a__isNatList(V2))) [2] a__U61(tt, zeros) -> a__U62(tt) [2] a__U61(tt, cons(V12, V22)) -> a__U62(a__U41(a__isNat(V12), V22)) [2] a__U61(tt, V2) -> a__U62(isNatIList(V2)) [2] a__U62(tt) -> tt [1] a__U71(tt, L, 0) -> a__U72(tt, L) [2] a__U71(tt, L, length(V13)) -> a__U72(a__U11(a__isNatList(V13)), L) [2] a__U71(tt, L, s(V14)) -> a__U72(a__U21(a__isNat(V14)), L) [2] a__U71(tt, L, N) -> a__U72(isNat(N), L) [2] a__U72(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, 0, N) -> a__U92(tt, IL, 0, N) [2] a__U91(tt, IL, length(V15), N) -> a__U92(a__U11(a__isNatList(V15)), IL, length(V15), N) [2] a__U91(tt, IL, s(V16), N) -> a__U92(a__U21(a__isNat(V16)), IL, s(V16), N) [2] a__U91(tt, IL, M, N) -> a__U92(isNat(M), IL, M, N) [2] a__U92(tt, IL, M, 0) -> a__U93(tt, IL, M, 0) [2] a__U92(tt, IL, M, length(V17)) -> a__U93(a__U11(a__isNatList(V17)), IL, M, length(V17)) [2] a__U92(tt, IL, M, s(V18)) -> a__U93(a__U21(a__isNat(V18)), IL, M, s(V18)) [2] a__U92(tt, IL, M, N) -> a__U93(isNat(N), IL, M, N) [2] a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__isNat(0) -> tt [1] a__isNat(length(nil)) -> a__U11(tt) [2] a__isNat(length(cons(V19, V23))) -> a__U11(a__U51(a__isNat(V19), V23)) [2] a__isNat(length(take(V110, V24))) -> a__U11(a__U61(a__isNat(V110), V24)) [2] a__isNat(length(V1)) -> a__U11(isNatList(V1)) [2] a__isNat(s(0)) -> a__U21(tt) [2] a__isNat(s(length(V111))) -> a__U21(a__U11(a__isNatList(V111))) [2] a__isNat(s(s(V112))) -> a__U21(a__U21(a__isNat(V112))) [2] a__isNat(s(V1)) -> a__U21(isNat(V1)) [2] a__isNatIList(nil) -> a__U31(tt) [2] a__isNatIList(cons(V113, V25)) -> a__U31(a__U51(a__isNat(V113), V25)) [2] a__isNatIList(take(V114, V26)) -> a__U31(a__U61(a__isNat(V114), V26)) [2] a__isNatIList(V) -> a__U31(isNatList(V)) [2] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(0, V2)) -> a__U41(tt, V2) [2] a__isNatIList(cons(length(V115), V2)) -> a__U41(a__U11(a__isNatList(V115)), V2) [2] a__isNatIList(cons(s(V116), V2)) -> a__U41(a__U21(a__isNat(V116)), V2) [2] a__isNatIList(cons(V1, V2)) -> a__U41(isNat(V1), V2) [2] a__isNatList(nil) -> tt [1] a__isNatList(cons(0, V2)) -> a__U51(tt, V2) [2] a__isNatList(cons(length(V117), V2)) -> a__U51(a__U11(a__isNatList(V117)), V2) [2] a__isNatList(cons(s(V118), V2)) -> a__U51(a__U21(a__isNat(V118)), V2) [2] a__isNatList(cons(V1, V2)) -> a__U51(isNat(V1), V2) [2] a__isNatList(take(0, V2)) -> a__U61(tt, V2) [2] a__isNatList(take(length(V119), V2)) -> a__U61(a__U11(a__isNatList(V119)), V2) [2] a__isNatList(take(s(V120), V2)) -> a__U61(a__U21(a__isNat(V120)), V2) [2] a__isNatList(take(V1, V2)) -> a__U61(isNat(V1), V2) [2] a__length(nil) -> 0 [1] a__length(cons(N, nil)) -> a__U71(tt, nil, N) [2] a__length(cons(N, cons(V121, V27))) -> a__U71(a__U51(a__isNat(V121), V27), cons(V121, V27), N) [2] a__length(cons(N, take(V122, V28))) -> a__U71(a__U61(a__isNat(V122), V28), take(V122, V28), N) [2] a__length(cons(N, L)) -> a__U71(isNatList(L), L, N) [2] a__take(0, IL) -> a__U81(a__U31(a__isNatList(IL))) [2] a__take(0, zeros) -> a__U81(tt) [2] a__take(0, cons(V123, V29)) -> a__U81(a__U41(a__isNat(V123), V29)) [2] a__take(0, IL) -> a__U81(isNatIList(IL)) [2] a__take(s(M), cons(N, IL)) -> a__U91(a__U31(a__isNatList(IL)), IL, M, N) [2] a__take(s(M), cons(N, zeros)) -> a__U91(tt, zeros, M, N) [2] a__take(s(M), cons(N, cons(V124, V210))) -> a__U91(a__U41(a__isNat(V124), V210), cons(V124, V210), M, N) [2] a__take(s(M), cons(N, IL)) -> a__U91(isNatIList(IL), IL, M, N) [2] mark(zeros) -> a__zeros [1] mark(U11(X)) -> a__U11(mark(X)) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X)) -> a__U31(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U42(X)) -> a__U42(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X)) -> a__U52(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U61(X1, X2)) -> a__U61(mark(X1), X2) [1] mark(U62(X)) -> a__U62(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2)) -> a__U72(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) [1] mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X) -> U11(X) [1] a__U21(X) -> U21(X) [1] a__U31(X) -> U31(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U42(X) -> U42(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X) -> U52(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U61(X1, X2) -> U61(X1, X2) [1] a__U62(X) -> U62(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2) -> U72(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) [1] a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 cons :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 0 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 tt :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U62 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U71 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U72 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNat :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 s :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__length :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 mark :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U81 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 nil :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U91 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U92 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U93 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 take :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 length :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__take :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U11 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U21 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U31 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U41 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U42 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNatIList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U51 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U52 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNatList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U61 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U62 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U71 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U72 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNat :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U81 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U91 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U92 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U93 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: a__U11(z) -{ 1 }-> 2 :|: z = 2 a__U11(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 2 :|: z = 2 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z) -{ 1 }-> 2 :|: z = 2 a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z') -{ 2 }-> a__U42(a__U41(a__isNat(V1'), V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U41(z, z') -{ 2 }-> a__U42(a__U31(a__isNatList(V2))) :|: z = 2, z' = V2, V2 >= 0 a__U41(z, z') -{ 2 }-> a__U42(2) :|: z = 2, z' = 3 a__U41(z, z') -{ 2 }-> a__U42(1 + V2) :|: z = 2, z' = V2, V2 >= 0 a__U41(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U42(z) -{ 1 }-> 2 :|: z = 2 a__U42(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z') -{ 2 }-> a__U52(a__U61(a__isNat(V11), V21)) :|: z = 2, V21 >= 0, V11 >= 0, z' = 1 + V11 + V21 a__U51(z, z') -{ 2 }-> a__U52(a__U51(a__isNat(V1''), V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2'' a__U51(z, z') -{ 2 }-> a__U52(2) :|: z = 2, z' = 1 a__U51(z, z') -{ 2 }-> a__U52(1 + V2) :|: z = 2, z' = V2, V2 >= 0 a__U51(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U52(z) -{ 1 }-> 2 :|: z = 2 a__U52(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U61(z, z') -{ 2 }-> a__U62(a__U41(a__isNat(V12), V22)) :|: z = 2, V22 >= 0, V12 >= 0, z' = 1 + V12 + V22 a__U61(z, z') -{ 2 }-> a__U62(a__U31(a__isNatList(V2))) :|: z = 2, z' = V2, V2 >= 0 a__U61(z, z') -{ 2 }-> a__U62(2) :|: z = 2, z' = 3 a__U61(z, z') -{ 2 }-> a__U62(1 + V2) :|: z = 2, z' = V2, V2 >= 0 a__U61(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U62(z) -{ 1 }-> 2 :|: z = 2 a__U62(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z', z'') -{ 2 }-> a__U72(a__U21(a__isNat(V14)), L) :|: z = 2, z'' = 1 + V14, V14 >= 0, L >= 0, z' = L a__U71(z, z', z'') -{ 2 }-> a__U72(a__U11(a__isNatList(V13)), L) :|: z = 2, V13 >= 0, z'' = 1 + V13, L >= 0, z' = L a__U71(z, z', z'') -{ 2 }-> a__U72(2, L) :|: z = 2, z'' = 0, L >= 0, z' = L a__U71(z, z', z'') -{ 2 }-> a__U72(1 + N, L) :|: z = 2, L >= 0, z'' = N, z' = L, N >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U72(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U72(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U91(z, z', z'', z1) -{ 2 }-> a__U92(a__U21(a__isNat(V16)), IL, 1 + V16, N) :|: z = 2, z1 = N, z'' = 1 + V16, z' = IL, V16 >= 0, IL >= 0, N >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(a__U11(a__isNatList(V15)), IL, 1 + V15, N) :|: z = 2, z'' = 1 + V15, z1 = N, z' = IL, V15 >= 0, IL >= 0, N >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(2, IL, 0, N) :|: z = 2, z'' = 0, z1 = N, z' = IL, IL >= 0, N >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(1 + M, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U92(z, z', z'', z1) -{ 2 }-> a__U93(a__U21(a__isNat(V18)), IL, M, 1 + V18) :|: z = 2, V18 >= 0, z1 = 1 + V18, z' = IL, M >= 0, IL >= 0, z'' = M a__U92(z, z', z'', z1) -{ 2 }-> a__U93(a__U11(a__isNatList(V17)), IL, M, 1 + V17) :|: z = 2, z1 = 1 + V17, z' = IL, M >= 0, V17 >= 0, IL >= 0, z'' = M a__U92(z, z', z'', z1) -{ 2 }-> a__U93(2, IL, M, 0) :|: z = 2, z1 = 0, z' = IL, M >= 0, IL >= 0, z'' = M a__U92(z, z', z'', z1) -{ 2 }-> a__U93(1 + N, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U92(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U93(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U93(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V112))) :|: z = 1 + (1 + V112), V112 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNatList(V111))) :|: z = 1 + (1 + V111), V111 >= 0 a__isNat(z) -{ 2 }-> a__U21(2) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U61(a__isNat(V110), V24)) :|: V110 >= 0, z = 1 + (1 + V110 + V24), V24 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U51(a__isNat(V19), V23)) :|: V19 >= 0, V23 >= 0, z = 1 + (1 + V19 + V23) a__isNat(z) -{ 2 }-> a__U11(2) :|: z = 1 + 1 a__isNat(z) -{ 2 }-> a__U11(1 + V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIList(z) -{ 2 }-> a__U41(a__U21(a__isNat(V116)), V2) :|: z = 1 + (1 + V116) + V2, V2 >= 0, V116 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__U11(a__isNatList(V115)), V2) :|: z = 1 + (1 + V115) + V2, V2 >= 0, V115 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(2, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatIList(z) -{ 2 }-> a__U41(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 2 }-> a__U31(a__U61(a__isNat(V114), V26)) :|: V114 >= 0, z = 1 + V114 + V26, V26 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(a__U51(a__isNat(V113), V25)) :|: V25 >= 0, z = 1 + V113 + V25, V113 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(2) :|: z = 1 a__isNatIList(z) -{ 2 }-> a__U31(1 + V) :|: z = V, V >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatList(z) -{ 2 }-> a__U61(a__U21(a__isNat(V120)), V2) :|: z = 1 + (1 + V120) + V2, V120 >= 0, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__U11(a__isNatList(V119)), V2) :|: V2 >= 0, V119 >= 0, z = 1 + (1 + V119) + V2 a__isNatList(z) -{ 2 }-> a__U61(2, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U61(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__U21(a__isNat(V118)), V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U51(a__U11(a__isNatList(V117)), V2) :|: V117 >= 0, V2 >= 0, z = 1 + (1 + V117) + V2 a__isNatList(z) -{ 2 }-> a__U51(2, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U51(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> a__U71(a__U61(a__isNat(V122), V28), 1 + V122 + V28, N) :|: V28 >= 0, z = 1 + N + (1 + V122 + V28), V122 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(a__U51(a__isNat(V121), V27), 1 + V121 + V27, N) :|: V121 >= 0, z = 1 + N + (1 + V121 + V27), V27 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(2, 1, N) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> a__U71(1 + L, L, N) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 2 }-> a__U91(a__U41(a__isNat(V124), V210), 1 + V124 + V210, M, N) :|: z' = 1 + N + (1 + V124 + V210), V124 >= 0, z = 1 + M, V210 >= 0, M >= 0, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__U31(a__isNatList(IL)), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U91(2, 3, M, N) :|: z = 1 + M, M >= 0, z' = 1 + N + 3, N >= 0 a__take(z, z') -{ 2 }-> a__U91(1 + IL, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U81(a__U41(a__isNat(V123), V29)) :|: z' = 1 + V123 + V29, V29 >= 0, z = 0, V123 >= 0 a__take(z, z') -{ 2 }-> a__U81(a__U31(a__isNatList(IL))) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 2 }-> a__U81(2) :|: z' = 3, z = 0 a__take(z, z') -{ 2 }-> a__U81(1 + IL) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U93(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U92(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U72(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U71(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U52(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U42(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U41(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U31(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (27) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: a__U11(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U11(z) -{ 1 }-> 2 :|: z = 2 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 2 :|: z = 2 a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z) -{ 1 }-> 2 :|: z = 2 a__U42(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U42(z) -{ 1 }-> 2 :|: z = 2 a__U52(z) -{ 1 }-> 2 :|: z = 2 a__U52(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U62(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U62(z) -{ 1 }-> 2 :|: z = 2 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: a__U11(z) -{ 1 }-> 2 :|: z = 2 a__U11(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 2 :|: z = 2 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z) -{ 1 }-> 2 :|: z = 2 a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z') -{ 2 }-> a__U42(a__U41(a__isNat(V1'), V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U41(z, z') -{ 2 }-> a__U42(a__U31(a__isNatList(V2))) :|: z = 2, z' = V2, V2 >= 0 a__U41(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U41(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2 a__U41(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U41(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X a__U41(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U42(z) -{ 1 }-> 2 :|: z = 2 a__U42(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z') -{ 2 }-> a__U52(a__U61(a__isNat(V11), V21)) :|: z = 2, V21 >= 0, V11 >= 0, z' = 1 + V11 + V21 a__U51(z, z') -{ 2 }-> a__U52(a__U51(a__isNat(V1''), V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2'' a__U51(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U51(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2 a__U51(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U51(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X a__U51(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U52(z) -{ 1 }-> 2 :|: z = 2 a__U52(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U61(z, z') -{ 2 }-> a__U62(a__U41(a__isNat(V12), V22)) :|: z = 2, V22 >= 0, V12 >= 0, z' = 1 + V12 + V22 a__U61(z, z') -{ 2 }-> a__U62(a__U31(a__isNatList(V2))) :|: z = 2, z' = V2, V2 >= 0 a__U61(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U61(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2 a__U61(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U61(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X a__U61(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U62(z) -{ 1 }-> 2 :|: z = 2 a__U62(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z', z'') -{ 2 }-> a__U72(a__U21(a__isNat(V14)), L) :|: z = 2, z'' = 1 + V14, V14 >= 0, L >= 0, z' = L a__U71(z, z', z'') -{ 2 }-> a__U72(a__U11(a__isNatList(V13)), L) :|: z = 2, V13 >= 0, z'' = 1 + V13, L >= 0, z' = L a__U71(z, z', z'') -{ 2 }-> a__U72(2, L) :|: z = 2, z'' = 0, L >= 0, z' = L a__U71(z, z', z'') -{ 2 }-> a__U72(1 + N, L) :|: z = 2, L >= 0, z'' = N, z' = L, N >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U72(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U72(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U91(z, z', z'', z1) -{ 2 }-> a__U92(a__U21(a__isNat(V16)), IL, 1 + V16, N) :|: z = 2, z1 = N, z'' = 1 + V16, z' = IL, V16 >= 0, IL >= 0, N >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(a__U11(a__isNatList(V15)), IL, 1 + V15, N) :|: z = 2, z'' = 1 + V15, z1 = N, z' = IL, V15 >= 0, IL >= 0, N >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(2, IL, 0, N) :|: z = 2, z'' = 0, z1 = N, z' = IL, IL >= 0, N >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(1 + M, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U92(z, z', z'', z1) -{ 2 }-> a__U93(a__U21(a__isNat(V18)), IL, M, 1 + V18) :|: z = 2, V18 >= 0, z1 = 1 + V18, z' = IL, M >= 0, IL >= 0, z'' = M a__U92(z, z', z'', z1) -{ 2 }-> a__U93(a__U11(a__isNatList(V17)), IL, M, 1 + V17) :|: z = 2, z1 = 1 + V17, z' = IL, M >= 0, V17 >= 0, IL >= 0, z'' = M a__U92(z, z', z'', z1) -{ 2 }-> a__U93(2, IL, M, 0) :|: z = 2, z1 = 0, z' = IL, M >= 0, IL >= 0, z'' = M a__U92(z, z', z'', z1) -{ 2 }-> a__U93(1 + N, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U92(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U93(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U93(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V112))) :|: z = 1 + (1 + V112), V112 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNatList(V111))) :|: z = 1 + (1 + V111), V111 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U61(a__isNat(V110), V24)) :|: V110 >= 0, z = 1 + (1 + V110 + V24), V24 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U51(a__isNat(V19), V23)) :|: V19 >= 0, V23 >= 0, z = 1 + (1 + V19 + V23) a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 3 }-> 2 :|: z = 1 + 1, 2 = 2 a__isNat(z) -{ 3 }-> 2 :|: z = 1 + V1, V1 >= 0, 1 + V1 = 2 a__isNat(z) -{ 3 }-> 2 :|: z = 1 + 0, 2 = 2 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 2 = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + V1, V1 >= 0, X >= 0, 1 + V1 = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 2 = X a__isNatIList(z) -{ 2 }-> a__U41(a__U21(a__isNat(V116)), V2) :|: z = 1 + (1 + V116) + V2, V2 >= 0, V116 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__U11(a__isNatList(V115)), V2) :|: z = 1 + (1 + V115) + V2, V2 >= 0, V115 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(2, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatIList(z) -{ 2 }-> a__U41(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 2 }-> a__U31(a__U61(a__isNat(V114), V26)) :|: V114 >= 0, z = 1 + V114 + V26, V26 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(a__U51(a__isNat(V113), V25)) :|: V25 >= 0, z = 1 + V113 + V25, V113 >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 3 }-> 2 :|: z = 1, 2 = 2 a__isNatIList(z) -{ 3 }-> 2 :|: z = V, V >= 0, 1 + V = 2 a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIList(z) -{ 3 }-> 1 + X :|: z = 1, X >= 0, 2 = X a__isNatIList(z) -{ 3 }-> 1 + X :|: z = V, V >= 0, X >= 0, 1 + V = X a__isNatList(z) -{ 2 }-> a__U61(a__U21(a__isNat(V120)), V2) :|: z = 1 + (1 + V120) + V2, V120 >= 0, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__U11(a__isNatList(V119)), V2) :|: V2 >= 0, V119 >= 0, z = 1 + (1 + V119) + V2 a__isNatList(z) -{ 2 }-> a__U61(2, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U61(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__U21(a__isNat(V118)), V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U51(a__U11(a__isNatList(V117)), V2) :|: V117 >= 0, V2 >= 0, z = 1 + (1 + V117) + V2 a__isNatList(z) -{ 2 }-> a__U51(2, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U51(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> a__U71(a__U61(a__isNat(V122), V28), 1 + V122 + V28, N) :|: V28 >= 0, z = 1 + N + (1 + V122 + V28), V122 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(a__U51(a__isNat(V121), V27), 1 + V121 + V27, N) :|: V121 >= 0, z = 1 + N + (1 + V121 + V27), V27 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(2, 1, N) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> a__U71(1 + L, L, N) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 2 }-> a__U91(a__U41(a__isNat(V124), V210), 1 + V124 + V210, M, N) :|: z' = 1 + N + (1 + V124 + V210), V124 >= 0, z = 1 + M, V210 >= 0, M >= 0, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__U31(a__isNatList(IL)), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U91(2, 3, M, N) :|: z = 1 + M, M >= 0, z' = 1 + N + 3, N >= 0 a__take(z, z') -{ 2 }-> a__U91(1 + IL, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U81(a__U41(a__isNat(V123), V29)) :|: z' = 1 + V123 + V29, V29 >= 0, z = 0, V123 >= 0 a__take(z, z') -{ 2 }-> a__U81(a__U31(a__isNatList(IL))) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 3 }-> 1 :|: z' = 3, z = 0, 2 = 2 a__take(z, z') -{ 3 }-> 1 :|: z' = IL, z = 0, IL >= 0, 1 + IL = 2 a__take(z, z') -{ 3 }-> 1 + X :|: z' = 3, z = 0, X >= 0, 2 = X a__take(z, z') -{ 3 }-> 1 + X :|: z' = IL, z = 0, IL >= 0, X >= 0, 1 + IL = X a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U93(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U92(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U72(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U71(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U52(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U42(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U41(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U31(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: a__U11(z) -{ 1 }-> 2 :|: z = 2 a__U11(z) -{ 1 }-> 1 + z :|: z >= 0 a__U21(z) -{ 1 }-> 2 :|: z = 2 a__U21(z) -{ 1 }-> 1 + z :|: z >= 0 a__U31(z) -{ 1 }-> 2 :|: z = 2 a__U31(z) -{ 1 }-> 1 + z :|: z >= 0 a__U41(z, z') -{ 2 }-> a__U42(a__U41(a__isNat(V1'), V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U41(z, z') -{ 2 }-> a__U42(a__U31(a__isNatList(z'))) :|: z = 2, z' >= 0 a__U41(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U41(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U41(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U41(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U41(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U42(z) -{ 1 }-> 2 :|: z = 2 a__U42(z) -{ 1 }-> 1 + z :|: z >= 0 a__U51(z, z') -{ 2 }-> a__U52(a__U61(a__isNat(V11), V21)) :|: z = 2, V21 >= 0, V11 >= 0, z' = 1 + V11 + V21 a__U51(z, z') -{ 2 }-> a__U52(a__U51(a__isNat(V1''), V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2'' a__U51(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U51(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U51(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U51(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U51(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U52(z) -{ 1 }-> 2 :|: z = 2 a__U52(z) -{ 1 }-> 1 + z :|: z >= 0 a__U61(z, z') -{ 2 }-> a__U62(a__U41(a__isNat(V12), V22)) :|: z = 2, V22 >= 0, V12 >= 0, z' = 1 + V12 + V22 a__U61(z, z') -{ 2 }-> a__U62(a__U31(a__isNatList(z'))) :|: z = 2, z' >= 0 a__U61(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U61(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U61(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U61(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U61(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U62(z) -{ 1 }-> 2 :|: z = 2 a__U62(z) -{ 1 }-> 1 + z :|: z >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U21(a__isNat(z'' - 1)), z') :|: z = 2, z'' - 1 >= 0, z' >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U11(a__isNatList(z'' - 1)), z') :|: z = 2, z'' - 1 >= 0, z' >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(2, z') :|: z = 2, z'' = 0, z' >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(1 + z'', z') :|: z = 2, z' >= 0, z'' >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U72(z, z') -{ 1 }-> 1 + a__length(mark(z')) :|: z = 2, z' >= 0 a__U72(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + z :|: z >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1), z1) :|: z = 2, z'' - 1 >= 0, z' >= 0, z1 >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(a__U11(a__isNatList(z'' - 1)), z', 1 + (z'' - 1), z1) :|: z = 2, z'' - 1 >= 0, z' >= 0, z1 >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(2, z', 0, z1) :|: z = 2, z'' = 0, z' >= 0, z1 >= 0 a__U91(z, z', z'', z1) -{ 2 }-> a__U92(1 + z'', z', z'', z1) :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__U92(z, z', z'', z1) -{ 2 }-> a__U93(a__U21(a__isNat(z1 - 1)), z', z'', 1 + (z1 - 1)) :|: z = 2, z1 - 1 >= 0, z'' >= 0, z' >= 0 a__U92(z, z', z'', z1) -{ 2 }-> a__U93(a__U11(a__isNatList(z1 - 1)), z', z'', 1 + (z1 - 1)) :|: z = 2, z'' >= 0, z1 - 1 >= 0, z' >= 0 a__U92(z, z', z'', z1) -{ 2 }-> a__U93(2, z', z'', 0) :|: z = 2, z1 = 0, z'' >= 0, z' >= 0 a__U92(z, z', z'', z1) -{ 2 }-> a__U93(1 + z1, z', z'', z1) :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U92(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__U93(z, z', z'', z1) -{ 1 }-> 1 + mark(z1) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U93(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(z - 2))) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNatList(z - 2))) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U61(a__isNat(V110), V24)) :|: V110 >= 0, z = 1 + (1 + V110 + V24), V24 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U51(a__isNat(V19), V23)) :|: V19 >= 0, V23 >= 0, z = 1 + (1 + V19 + V23) a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 3 }-> 2 :|: z = 1 + 1, 2 = 2 a__isNat(z) -{ 3 }-> 2 :|: z - 1 >= 0, 1 + (z - 1) = 2 a__isNat(z) -{ 3 }-> 2 :|: z = 1 + 0, 2 = 2 a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 2 = X a__isNat(z) -{ 3 }-> 1 + X :|: z - 1 >= 0, X >= 0, 1 + (z - 1) = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 2 = X a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__U21(a__isNat(V116)), V2) :|: z = 1 + (1 + V116) + V2, V2 >= 0, V116 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__U11(a__isNatList(V115)), V2) :|: z = 1 + (1 + V115) + V2, V2 >= 0, V115 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(2, z - 1) :|: z - 1 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 2 }-> a__U31(a__U61(a__isNat(V114), V26)) :|: V114 >= 0, z = 1 + V114 + V26, V26 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(a__U51(a__isNat(V113), V25)) :|: V25 >= 0, z = 1 + V113 + V25, V113 >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 3 }-> 2 :|: z = 1, 2 = 2 a__isNatIList(z) -{ 3 }-> 2 :|: z >= 0, 1 + z = 2 a__isNatIList(z) -{ 3 }-> 1 + X :|: z = 1, X >= 0, 2 = X a__isNatIList(z) -{ 3 }-> 1 + X :|: z >= 0, X >= 0, 1 + z = X a__isNatIList(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__U21(a__isNat(V120)), V2) :|: z = 1 + (1 + V120) + V2, V120 >= 0, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__U11(a__isNatList(V119)), V2) :|: V2 >= 0, V119 >= 0, z = 1 + (1 + V119) + V2 a__isNatList(z) -{ 2 }-> a__U61(2, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 2 }-> a__U61(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__U21(a__isNat(V118)), V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U51(a__U11(a__isNatList(V117)), V2) :|: V117 >= 0, V2 >= 0, z = 1 + (1 + V117) + V2 a__isNatList(z) -{ 2 }-> a__U51(2, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 2 }-> a__U51(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + z :|: z >= 0 a__length(z) -{ 2 }-> a__U71(a__U61(a__isNat(V122), V28), 1 + V122 + V28, N) :|: V28 >= 0, z = 1 + N + (1 + V122 + V28), V122 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(a__U51(a__isNat(V121), V27), 1 + V121 + V27, N) :|: V121 >= 0, z = 1 + N + (1 + V121 + V27), V27 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(2, 1, z - 2) :|: z - 2 >= 0 a__length(z) -{ 2 }-> a__U71(1 + L, L, N) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 2 }-> a__U91(a__U41(a__isNat(V124), V210), 1 + V124 + V210, z - 1, N) :|: z' = 1 + N + (1 + V124 + V210), V124 >= 0, V210 >= 0, z - 1 >= 0, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__U31(a__isNatList(IL)), IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U91(2, 3, z - 1, z' - 4) :|: z - 1 >= 0, z' - 4 >= 0 a__take(z, z') -{ 2 }-> a__U91(1 + IL, IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U81(a__U41(a__isNat(V123), V29)) :|: z' = 1 + V123 + V29, V29 >= 0, z = 0, V123 >= 0 a__take(z, z') -{ 2 }-> a__U81(a__U31(a__isNatList(z'))) :|: z = 0, z' >= 0 a__take(z, z') -{ 3 }-> 1 :|: z' = 3, z = 0, 2 = 2 a__take(z, z') -{ 3 }-> 1 :|: z = 0, z' >= 0, 1 + z' = 2 a__take(z, z') -{ 3 }-> 1 + X :|: z' = 3, z = 0, X >= 0, 2 = X a__take(z, z') -{ 3 }-> 1 + X :|: z = 0, z' >= 0, X >= 0, 1 + z' = X a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNatList(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNatIList(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U93(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U92(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U72(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U71(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U52(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U42(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U41(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U31(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U21(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U11(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (31) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt) -> tt [1] a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) [1] a__U42(tt) -> tt [1] a__U51(tt, V2) -> a__U52(a__isNatList(V2)) [1] a__U52(tt) -> tt [1] a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) [1] a__U62(tt) -> tt [1] a__U71(tt, L, N) -> a__U72(a__isNat(N), L) [1] a__U72(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) [1] a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) [1] a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNatIList(V) -> a__U31(a__isNatList(V)) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) [1] a__take(0, IL) -> a__U81(a__isNatIList(IL)) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X)) -> a__U11(mark(X)) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X)) -> a__U31(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U42(X)) -> a__U42(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2)) -> a__U51(mark(X1), X2) [1] mark(U52(X)) -> a__U52(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U61(X1, X2)) -> a__U61(mark(X1), X2) [1] mark(U62(X)) -> a__U62(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2)) -> a__U72(mark(X1), X2) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) [1] mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X) -> U11(X) [1] a__U21(X) -> U21(X) [1] a__U31(X) -> U31(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U42(X) -> U42(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2) -> U51(X1, X2) [1] a__U52(X) -> U52(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U61(X1, X2) -> U61(X1, X2) [1] a__U62(X) -> U62(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2) -> U72(X1, X2) [1] a__isNat(X) -> isNat(X) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__U92(X1, X2, X3, X4) -> U92(X1, X2, X3, X4) [1] a__U93(X1, X2, X3, X4) -> U93(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 cons :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 0 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 zeros :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 tt :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 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0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U72 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 isNat :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U81 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U91 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U92 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 U93 :: 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 -> 0:zeros:cons:tt:s:nil:take:length:U11:U21:U31:U41:U42:isNatIList:U51:U52:isNatList:U61:U62:U71:U72:isNat:U81:U91:U92:U93 Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: a__U11(z) -{ 1 }-> 2 :|: z = 2 a__U11(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 2 :|: z = 2 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z) -{ 1 }-> 2 :|: z = 2 a__U31(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z') -{ 1 }-> a__U42(a__isNatIList(V2)) :|: z = 2, z' = V2, V2 >= 0 a__U41(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U42(z) -{ 1 }-> 2 :|: z = 2 a__U42(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z') -{ 1 }-> a__U52(a__isNatList(V2)) :|: z = 2, z' = V2, V2 >= 0 a__U51(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U52(z) -{ 1 }-> 2 :|: z = 2 a__U52(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U61(z, z') -{ 1 }-> a__U62(a__isNatIList(V2)) :|: z = 2, z' = V2, V2 >= 0 a__U61(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U62(z) -{ 1 }-> 2 :|: z = 2 a__U62(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z', z'') -{ 1 }-> a__U72(a__isNat(N), L) :|: z = 2, L >= 0, z'' = N, z' = L, N >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U72(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U72(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U91(z, z', z'', z1) -{ 1 }-> a__U92(a__isNat(M), IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U92(z, z', z'', z1) -{ 1 }-> a__U93(a__isNat(N), IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U92(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U93(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U93(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 1 }-> a__U21(a__isNat(V1)) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__U11(a__isNatList(V1)) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIList(z) -{ 1 }-> a__U41(a__isNat(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 1 }-> a__U31(a__isNatList(V)) :|: z = V, V >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatList(z) -{ 1 }-> a__U61(a__isNat(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> a__U51(a__isNat(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 1 }-> a__U71(a__isNatList(L), L, N) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U91(a__isNatIList(IL), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 1 }-> a__U81(a__isNatIList(IL)) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U93(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U92(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U72(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U71(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U62(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U61(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U52(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U51(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U42(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U41(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U31(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0) -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0) -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 S tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt) -> c2 A__U11(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt) -> c6 A__U31(z0) -> c7 A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U41(z0, z1) -> c9 A__U42(tt) -> c10 A__U42(z0) -> c11 A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U51(z0, z1) -> c13 A__U52(tt) -> c14 A__U52(z0) -> c15 A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U61(z0, z1) -> c17 A__U62(tt) -> c18 A__U62(z0) -> c19 A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c21 A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U72(z0, z1) -> c23 A__U81(tt) -> c24 A__U81(z0) -> c25 A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U91(z0, z1, z2, z3) -> c27 A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U92(z0, z1, z2, z3) -> c29 A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__U93(z0, z1, z2, z3) -> c31 A__ISNAT(0) -> c32 A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(z0) -> c35 A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(zeros) -> c37 A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATILIST(z0) -> c39 A__ISNATLIST(nil) -> c40 A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(z0) -> c43 A__LENGTH(nil) -> c44 A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__LENGTH(z0) -> c46 A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c49 MARK(zeros) -> c50(A__ZEROS) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(0) -> c73 MARK(tt) -> c74 MARK(s(z0)) -> c75(MARK(z0)) MARK(nil) -> c76 K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__U11_1, A__U21_1, A__U31_1, A__U41_2, A__U42_1, A__U51_2, A__U52_1, A__U61_2, A__U62_1, A__U71_3, A__U72_2, A__U81_1, A__U91_4, A__U92_4, A__U93_4, A__ISNAT_1, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8_2, c9, c10, c11, c12_2, c13, c14, c15, c16_2, c17, c18, c19, c20_2, c21, c22_2, c23, c24, c25, c26_2, c27, c28_2, c29, c30_1, c31, c32, c33_2, c34_2, c35, c36_2, c37, c38_2, c39, c40, c41_2, c42_2, c43, c44, c45_2, c46, c47_2, c48_2, c49, c50_1, c51_2, c52_2, c53_2, c54_2, c55_2, c56_1, c57_2, c58_2, c59_1, c60_2, c61_2, c62_2, c63_2, c64_1, c65_2, c66_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c73, c74, c75_1, c76 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 37 trailing nodes: A__U92(z0, z1, z2, z3) -> c29 A__U42(z0) -> c11 A__U42(tt) -> c10 MARK(nil) -> c76 A__ISNAT(0) -> c32 A__U52(z0) -> c15 MARK(zeros) -> c50(A__ZEROS) A__LENGTH(nil) -> c44 A__U61(z0, z1) -> c17 A__LENGTH(z0) -> c46 A__ISNATLIST(z0) -> c43 MARK(tt) -> c74 A__U62(z0) -> c19 A__U21(z0) -> c5 A__U71(z0, z1, z2) -> c21 A__U93(z0, z1, z2, z3) -> c31 A__U11(z0) -> c3 A__U31(tt) -> c6 A__ZEROS -> c A__U51(z0, z1) -> c13 A__U41(z0, z1) -> c9 A__ISNATLIST(nil) -> c40 A__U72(z0, z1) -> c23 A__U81(z0) -> c25 A__U21(tt) -> c4 A__TAKE(z0, z1) -> c49 A__U81(tt) -> c24 A__ISNATILIST(z0) -> c39 A__U62(tt) -> c18 A__U52(tt) -> c14 A__U11(tt) -> c2 A__U31(z0) -> c7 A__ZEROS -> c1 A__U91(z0, z1, z2, z3) -> c27 A__ISNAT(z0) -> c35 A__ISNATILIST(zeros) -> c37 MARK(0) -> c73 ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) S tuples: A__U41(tt, z0) -> c8(A__U42(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__U52(a__isNatList(z0)), A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__U62(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNAT(length(z0)) -> c33(A__U11(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__U31(a__isNatList(z0)), A__ISNATLIST(z0)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(0, z0) -> c47(A__U81(a__isNatIList(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U11(z0)) -> c51(A__U11(mark(z0)), MARK(z0)) MARK(U21(z0)) -> c52(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0)) -> c53(A__U31(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(U42(z0)) -> c55(A__U42(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(U52(z0)) -> c58(A__U52(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U62(z0)) -> c61(A__U62(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c66(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U41_2, A__U51_2, A__U61_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__U93_4, A__ISNAT_1, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c8_2, c12_2, c16_2, c20_2, c22_2, c26_2, c28_2, c30_1, c33_2, c34_2, c36_2, c38_2, c41_2, c42_2, c45_2, c47_2, c48_2, c51_2, c52_2, c53_2, c54_2, c55_2, c56_1, c57_2, c58_2, c59_1, c60_2, c61_2, c62_2, c63_2, c64_1, c65_2, c66_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) S tuples: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1 Compound Symbols: c20_2, c22_2, c26_2, c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1 ---------------------------------------- (41) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (42) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (43) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (44) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (45) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (46) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) [1] A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) [1] A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) [1] A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) [1] A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) [1] MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) [1] MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c64(A__ISNAT(z0)) [1] MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c72(MARK(z0)) [1] MARK(s(z0)) -> c75(MARK(z0)) [1] A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) [1] A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) [1] A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) [1] A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) [1] A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) [1] A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) [1] MARK(U11(z0)) -> c51(MARK(z0)) [1] MARK(U21(z0)) -> c52(MARK(z0)) [1] MARK(U31(z0)) -> c53(MARK(z0)) [1] MARK(U42(z0)) -> c55(MARK(z0)) [1] MARK(U52(z0)) -> c58(MARK(z0)) [1] MARK(U62(z0)) -> c61(MARK(z0)) [1] MARK(U81(z0)) -> c66(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt) -> tt [0] a__U11(z0) -> U11(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt) -> tt [0] a__U31(z0) -> U31(z0) [0] a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U42(tt) -> tt [0] a__U42(z0) -> U42(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatList(z0)) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt) -> tt [0] a__U52(z0) -> U52(z0) [0] a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) [0] a__U61(z0, z1) -> U61(z0, z1) [0] a__U62(tt) -> tt [0] a__U62(z0) -> U62(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0) -> s(a__length(mark(z0))) [0] a__U72(z0, z1) -> U72(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) [0] a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) [0] a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatList(z0)) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__isNatIList(z0)) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0)) -> a__U11(mark(z0)) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0)) -> a__U31(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U42(z0)) -> a__U42(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0)) -> a__U52(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0] mark(U62(z0)) -> a__U62(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1)) -> a__U72(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) [0] mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] Rewrite Strategy: INNERMOST ---------------------------------------- (47) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (48) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) [1] A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) [1] A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) [1] A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) [1] A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) [1] MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) [1] MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c64(A__ISNAT(z0)) [1] MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c72(MARK(z0)) [1] MARK(s(z0)) -> c75(MARK(z0)) [1] A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) [1] A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) [1] A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) [1] A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) [1] A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) [1] A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) [1] MARK(U11(z0)) -> c51(MARK(z0)) [1] MARK(U21(z0)) -> c52(MARK(z0)) [1] MARK(U31(z0)) -> c53(MARK(z0)) [1] MARK(U42(z0)) -> c55(MARK(z0)) [1] MARK(U52(z0)) -> c58(MARK(z0)) [1] MARK(U62(z0)) -> c61(MARK(z0)) [1] MARK(U81(z0)) -> c66(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt) -> tt [0] a__U11(z0) -> U11(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt) -> tt [0] a__U31(z0) -> U31(z0) [0] a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U42(tt) -> tt [0] a__U42(z0) -> U42(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatList(z0)) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt) -> tt [0] a__U52(z0) -> U52(z0) [0] a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) [0] a__U61(z0, z1) -> U61(z0, z1) [0] a__U62(tt) -> tt [0] a__U62(z0) -> U62(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0) -> s(a__length(mark(z0))) [0] a__U72(z0, z1) -> U72(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) [0] a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) [0] a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatList(z0)) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__isNatIList(z0)) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0)) -> a__U11(mark(z0)) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0)) -> a__U31(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U42(z0)) -> a__U42(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0)) -> a__U52(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0] mark(U62(z0)) -> a__U62(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1)) -> a__U72(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) [0] mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] The TRS has the following type information: A__U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c20 tt :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c20 :: c22 -> c33:c34 -> c20 A__U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c22 a__isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil A__ISNAT :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c33:c34 c22 :: c45 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c22 A__LENGTH :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c45 mark :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil MARK :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 A__U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c26 c26 :: c28 -> c33:c34 -> c26 A__U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c28 c28 :: c30 -> c33:c34 -> c28 A__U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c30 c30 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c30 A__ISNATILIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c38:c36 cons :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c38 :: c8 -> c33:c34 -> c38:c36 A__U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c8 A__ISNATLIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c41:c42 c41 :: c12 -> c33:c34 -> c41:c42 A__U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c12 take :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c42 :: c16 -> c33:c34 -> c41:c42 A__U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c16 c45 :: c20 -> c41:c42 -> c45 a__isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil A__TAKE :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> c48:c47 s :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c48 :: c26 -> c38:c36 -> c48:c47 a__isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c54 :: c8 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c56 :: c38:c36 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c57 :: c12 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c59 :: c41:c42 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c60 :: c16 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c62 :: c20 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c63 :: c22 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c64 :: c33:c34 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 length :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c65 :: c45 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c67 :: c26 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c68 :: c28 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c69 :: c30 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c70 :: c48:c47 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c71 :: c48:c47 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c72 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c75 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c8 :: c38:c36 -> c8 c12 :: c41:c42 -> c12 c16 :: c38:c36 -> c16 c33 :: c41:c42 -> c33:c34 c34 :: c33:c34 -> c33:c34 c36 :: c41:c42 -> c38:c36 0 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c47 :: c38:c36 -> c48:c47 U11 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c51 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U21 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c52 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U31 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c53 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U42 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c55 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U52 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c58 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U62 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c61 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U81 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil c66 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 a__zeros :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil zeros :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U11 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U21 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U31 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U42 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U52 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U62 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__length :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U81 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil nil :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil a__take :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil Rewrite Strategy: INNERMOST ---------------------------------------- (49) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__U71_3 A__U72_2 A__U91_4 A__U92_4 A__U93_4 A__ISNATILIST_1 A__ISNATLIST_1 A__LENGTH_1 A__TAKE_2 MARK_1 A__U41_2 A__U51_2 A__U61_2 A__ISNAT_1 (c) The following functions are completely defined: a__zeros a__U11_1 a__U21_1 a__U31_1 a__U41_2 a__U42_1 a__U51_2 a__U52_1 a__U61_2 a__U62_1 a__U71_3 a__U72_2 a__U81_1 a__U91_4 a__U92_4 a__U93_4 a__isNat_1 a__isNatIList_1 a__isNatList_1 a__length_1 a__take_2 mark_1 Due to the following rules being added: a__zeros -> null_a__zeros [0] a__U11(v0) -> null_a__U11 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0) -> null_a__U31 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U42(v0) -> null_a__U42 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0) -> null_a__U52 [0] a__U61(v0, v1) -> null_a__U61 [0] a__U62(v0) -> null_a__U62 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1) -> null_a__U72 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__U92(v0, v1, v2, v3) -> null_a__U92 [0] a__U93(v0, v1, v2, v3) -> null_a__U93 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__zeros, null_a__U11, null_a__U21, null_a__U31, null_a__U41, null_a__U42, null_a__U51, null_a__U52, null_a__U61, null_a__U62, null_a__U71, null_a__U72, null_a__U81, null_a__U91, null_a__U92, null_a__U93, null_a__isNat, null_a__isNatIList, null_a__isNatList, null_a__length, null_a__take, null_mark, const, const1, const2, const3, const4, const5, const6, const7, const8, const9, const10, const11, const12, const13 ---------------------------------------- (50) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) [1] A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) [1] A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) [1] A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) [1] A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) [1] MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) [1] MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c64(A__ISNAT(z0)) [1] MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c72(MARK(z0)) [1] MARK(s(z0)) -> c75(MARK(z0)) [1] A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) [1] A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) [1] A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) [1] A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) [1] A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) [1] A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) [1] MARK(U11(z0)) -> c51(MARK(z0)) [1] MARK(U21(z0)) -> c52(MARK(z0)) [1] MARK(U31(z0)) -> c53(MARK(z0)) [1] MARK(U42(z0)) -> c55(MARK(z0)) [1] MARK(U52(z0)) -> c58(MARK(z0)) [1] MARK(U62(z0)) -> c61(MARK(z0)) [1] MARK(U81(z0)) -> c66(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt) -> tt [0] a__U11(z0) -> U11(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt) -> tt [0] a__U31(z0) -> U31(z0) [0] a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U42(tt) -> tt [0] a__U42(z0) -> U42(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatList(z0)) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt) -> tt [0] a__U52(z0) -> U52(z0) [0] a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) [0] a__U61(z0, z1) -> U61(z0, z1) [0] a__U62(tt) -> tt [0] a__U62(z0) -> U62(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0) -> s(a__length(mark(z0))) [0] a__U72(z0, z1) -> U72(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) [0] a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) [0] a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatList(z0)) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__isNatIList(z0)) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0)) -> a__U11(mark(z0)) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0)) -> a__U31(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U42(z0)) -> a__U42(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0)) -> a__U52(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0] mark(U62(z0)) -> a__U62(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1)) -> a__U72(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) [0] mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0) -> null_a__U11 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0) -> null_a__U31 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U42(v0) -> null_a__U42 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0) -> null_a__U52 [0] a__U61(v0, v1) -> null_a__U61 [0] a__U62(v0) -> null_a__U62 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1) -> null_a__U72 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__U92(v0, v1, v2, v3) -> null_a__U92 [0] a__U93(v0, v1, v2, v3) -> null_a__U93 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c20 tt :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c20 :: c22 -> c33:c34 -> c20 A__U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c22 a__isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNAT :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c33:c34 c22 :: c45 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c22 A__LENGTH :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c45 mark :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark MARK :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 A__U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c26 c26 :: c28 -> c33:c34 -> c26 A__U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c28 c28 :: c30 -> c33:c34 -> c28 A__U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c30 c30 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c30 A__ISNATILIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c38:c36 cons :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c38 :: c8 -> c33:c34 -> c38:c36 A__U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c8 A__ISNATLIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c41:c42 c41 :: c12 -> c33:c34 -> c41:c42 A__U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c12 take :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c42 :: c16 -> c33:c34 -> c41:c42 A__U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c16 c45 :: c20 -> c41:c42 -> c45 a__isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark A__TAKE :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c48:c47 s :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c48 :: c26 -> c38:c36 -> c48:c47 a__isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c54 :: c8 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c56 :: c38:c36 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c57 :: c12 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c59 :: c41:c42 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c60 :: c16 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c62 :: c20 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c63 :: c22 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c64 :: c33:c34 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 length :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c65 :: c45 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c67 :: c26 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c68 :: c28 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c69 :: c30 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c70 :: c48:c47 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c71 :: c48:c47 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c72 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c75 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 c8 :: c38:c36 -> c8 c12 :: c41:c42 -> c12 c16 :: c38:c36 -> c16 c33 :: c41:c42 -> c33:c34 c34 :: c33:c34 -> c33:c34 c36 :: c41:c42 -> c38:c36 0 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c47 :: c38:c36 -> c48:c47 U11 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c51 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U21 :: 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__zeros :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U11 :: 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U52 :: 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U81 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U91 :: 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_mark :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark const :: c20 const1 :: c22 const2 :: c33:c34 const3 :: c45 const4 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 const5 :: c26 const6 :: c28 const7 :: c30 const8 :: c38:c36 const9 :: c8 const10 :: c41:c42 const11 :: c12 const12 :: c16 const13 :: c48:c47 Rewrite Strategy: INNERMOST ---------------------------------------- (51) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (52) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U71(tt, z0, 0) -> c20(A__U72(tt, z0), A__ISNAT(0)) [1] A__U71(tt, z0, length(z0')) -> c20(A__U72(a__U11(a__isNatList(z0')), z0), A__ISNAT(length(z0'))) [1] A__U71(tt, z0, s(z0'')) -> c20(A__U72(a__U21(a__isNat(z0'')), z0), A__ISNAT(s(z0''))) [1] A__U71(tt, z0, z1) -> c20(A__U72(isNat(z1), z0), A__ISNAT(z1)) [1] A__U71(tt, z0, z1) -> c20(A__U72(null_a__isNat, z0), A__ISNAT(z1)) [1] A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, 0, z2) -> c26(A__U92(tt, z0, 0, z2), A__ISNAT(0)) [1] A__U91(tt, z0, length(z023), z2) -> c26(A__U92(a__U11(a__isNatList(z023)), z0, length(z023), z2), A__ISNAT(length(z023))) [1] A__U91(tt, z0, s(z024), z2) -> c26(A__U92(a__U21(a__isNat(z024)), z0, s(z024), z2), A__ISNAT(s(z024))) [1] A__U91(tt, z0, z1, z2) -> c26(A__U92(isNat(z1), z0, z1, z2), A__ISNAT(z1)) [1] A__U91(tt, z0, z1, z2) -> c26(A__U92(null_a__isNat, z0, z1, z2), A__ISNAT(z1)) [1] A__U92(tt, z0, z1, 0) -> c28(A__U93(tt, z0, z1, 0), A__ISNAT(0)) [1] A__U92(tt, z0, z1, length(z025)) -> c28(A__U93(a__U11(a__isNatList(z025)), z0, z1, length(z025)), A__ISNAT(length(z025))) [1] A__U92(tt, z0, z1, s(z026)) -> c28(A__U93(a__U21(a__isNat(z026)), z0, z1, s(z026)), A__ISNAT(s(z026))) [1] A__U92(tt, z0, z1, z2) -> c28(A__U93(isNat(z2), z0, z1, z2), A__ISNAT(z2)) [1] A__U92(tt, z0, z1, z2) -> c28(A__U93(null_a__isNat, z0, z1, z2), A__ISNAT(z2)) [1] A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) [1] A__ISNATILIST(cons(0, z1)) -> c38(A__U41(tt, z1), A__ISNAT(0)) [1] A__ISNATILIST(cons(length(z027), z1)) -> c38(A__U41(a__U11(a__isNatList(z027)), z1), A__ISNAT(length(z027))) [1] A__ISNATILIST(cons(s(z028), z1)) -> c38(A__U41(a__U21(a__isNat(z028)), z1), A__ISNAT(s(z028))) [1] A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(null_a__isNat, z1), A__ISNAT(z0)) [1] A__ISNATLIST(cons(0, z1)) -> c41(A__U51(tt, z1), A__ISNAT(0)) [1] A__ISNATLIST(cons(length(z029), z1)) -> c41(A__U51(a__U11(a__isNatList(z029)), z1), A__ISNAT(length(z029))) [1] A__ISNATLIST(cons(s(z030), z1)) -> c41(A__U51(a__U21(a__isNat(z030)), z1), A__ISNAT(s(z030))) [1] A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(null_a__isNat, z1), A__ISNAT(z0)) [1] A__ISNATLIST(take(0, z1)) -> c42(A__U61(tt, z1), A__ISNAT(0)) [1] A__ISNATLIST(take(length(z031), z1)) -> c42(A__U61(a__U11(a__isNatList(z031)), z1), A__ISNAT(length(z031))) [1] A__ISNATLIST(take(s(z032), z1)) -> c42(A__U61(a__U21(a__isNat(z032)), z1), A__ISNAT(s(z032))) [1] A__ISNATLIST(take(z0, z1)) -> c42(A__U61(isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c42(A__U61(null_a__isNat, z1), A__ISNAT(z0)) [1] A__LENGTH(cons(z0, nil)) -> c45(A__U71(tt, nil, z0), A__ISNATLIST(nil)) [1] A__LENGTH(cons(z0, cons(z033, z19))) -> c45(A__U71(a__U51(a__isNat(z033), z19), cons(z033, z19), z0), A__ISNATLIST(cons(z033, z19))) [1] A__LENGTH(cons(z0, take(z034, z110))) -> c45(A__U71(a__U61(a__isNat(z034), z110), take(z034, z110), z0), A__ISNATLIST(take(z034, z110))) [1] A__LENGTH(cons(z0, z1)) -> c45(A__U71(isNatList(z1), z1, z0), A__ISNATLIST(z1)) [1] A__LENGTH(cons(z0, z1)) -> c45(A__U71(null_a__isNatList, z1, z0), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__U31(a__isNatList(z2)), z2, z0, z1), A__ISNATILIST(z2)) [1] A__TAKE(s(z0), cons(z1, zeros)) -> c48(A__U91(tt, zeros, z0, z1), A__ISNATILIST(zeros)) [1] A__TAKE(s(z0), cons(z1, cons(z035, z111))) -> c48(A__U91(a__U41(a__isNat(z035), z111), cons(z035, z111), z0, z1), A__ISNATILIST(cons(z035, z111))) [1] A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(null_a__isNatIList, z2, z0, z1), A__ISNATILIST(z2)) [1] MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) [1] MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c64(A__ISNAT(z0)) [1] MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c72(MARK(z0)) [1] MARK(s(z0)) -> c75(MARK(z0)) [1] A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) [1] A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) [1] A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) [1] A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) [1] A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) [1] A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) [1] MARK(U11(z0)) -> c51(MARK(z0)) [1] MARK(U21(z0)) -> c52(MARK(z0)) [1] MARK(U31(z0)) -> c53(MARK(z0)) [1] MARK(U42(z0)) -> c55(MARK(z0)) [1] MARK(U52(z0)) -> c58(MARK(z0)) [1] MARK(U62(z0)) -> c61(MARK(z0)) [1] MARK(U81(z0)) -> c66(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt) -> tt [0] a__U11(z0) -> U11(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt) -> tt [0] a__U31(z0) -> U31(z0) [0] a__U41(tt, z0) -> a__U42(a__U31(a__isNatList(z0))) [0] a__U41(tt, zeros) -> a__U42(tt) [0] a__U41(tt, cons(z01466, z1662)) -> a__U42(a__U41(a__isNat(z01466), z1662)) [0] a__U41(tt, z0) -> a__U42(isNatIList(z0)) [0] a__U41(tt, z0) -> a__U42(null_a__isNatIList) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U42(tt) -> tt [0] a__U42(z0) -> U42(z0) [0] a__U51(tt, nil) -> a__U52(tt) [0] a__U51(tt, cons(z01467, z1663)) -> a__U52(a__U51(a__isNat(z01467), z1663)) [0] a__U51(tt, take(z01468, z1664)) -> a__U52(a__U61(a__isNat(z01468), z1664)) [0] a__U51(tt, z0) -> a__U52(isNatList(z0)) [0] a__U51(tt, z0) -> a__U52(null_a__isNatList) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt) -> tt [0] a__U52(z0) -> U52(z0) [0] a__U61(tt, z0) -> a__U62(a__U31(a__isNatList(z0))) [0] a__U61(tt, zeros) -> a__U62(tt) [0] a__U61(tt, cons(z01469, z1665)) -> a__U62(a__U41(a__isNat(z01469), z1665)) [0] a__U61(tt, z0) -> a__U62(isNatIList(z0)) [0] a__U61(tt, z0) -> a__U62(null_a__isNatIList) [0] a__U61(z0, z1) -> U61(z0, z1) [0] a__U62(tt) -> tt [0] a__U62(z0) -> U62(z0) [0] a__U71(tt, z0, 0) -> a__U72(tt, z0) [0] a__U71(tt, z0, length(z01470)) -> a__U72(a__U11(a__isNatList(z01470)), z0) [0] a__U71(tt, z0, s(z01471)) -> a__U72(a__U21(a__isNat(z01471)), z0) [0] a__U71(tt, z0, z1) -> a__U72(isNat(z1), z0) [0] a__U71(tt, z0, z1) -> a__U72(null_a__isNat, z0) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0) -> s(a__length(mark(z0))) [0] a__U72(z0, z1) -> U72(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, 0, z2) -> a__U92(tt, z0, 0, z2) [0] a__U91(tt, z0, length(z01494), z2) -> a__U92(a__U11(a__isNatList(z01494)), z0, length(z01494), z2) [0] a__U91(tt, z0, s(z01495), z2) -> a__U92(a__U21(a__isNat(z01495)), z0, s(z01495), z2) [0] a__U91(tt, z0, z1, z2) -> a__U92(isNat(z1), z0, z1, z2) [0] a__U91(tt, z0, z1, z2) -> a__U92(null_a__isNat, z0, z1, z2) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__U92(tt, z0, z1, 0) -> a__U93(tt, z0, z1, 0) [0] a__U92(tt, z0, z1, length(z01496)) -> a__U93(a__U11(a__isNatList(z01496)), z0, z1, length(z01496)) [0] a__U92(tt, z0, z1, s(z01497)) -> a__U93(a__U21(a__isNat(z01497)), z0, z1, s(z01497)) [0] a__U92(tt, z0, z1, z2) -> a__U93(isNat(z2), z0, z1, z2) [0] a__U92(tt, z0, z1, z2) -> a__U93(null_a__isNat, z0, z1, z2) [0] a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) [0] a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) [0] a__isNat(0) -> tt [0] a__isNat(length(nil)) -> a__U11(tt) [0] a__isNat(length(cons(z01498, z1676))) -> a__U11(a__U51(a__isNat(z01498), z1676)) [0] a__isNat(length(take(z01499, z1677))) -> a__U11(a__U61(a__isNat(z01499), z1677)) [0] a__isNat(length(z0)) -> a__U11(isNatList(z0)) [0] a__isNat(length(z0)) -> a__U11(null_a__isNatList) [0] a__isNat(s(0)) -> a__U21(tt) [0] a__isNat(s(length(z01500))) -> a__U21(a__U11(a__isNatList(z01500))) [0] a__isNat(s(s(z01501))) -> a__U21(a__U21(a__isNat(z01501))) [0] a__isNat(s(z0)) -> a__U21(isNat(z0)) [0] a__isNat(s(z0)) -> a__U21(null_a__isNat) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(nil) -> a__U31(tt) [0] a__isNatIList(cons(z01502, z1678)) -> a__U31(a__U51(a__isNat(z01502), z1678)) [0] a__isNatIList(take(z01503, z1679)) -> a__U31(a__U61(a__isNat(z01503), z1679)) [0] a__isNatIList(z0) -> a__U31(isNatList(z0)) [0] a__isNatIList(z0) -> a__U31(null_a__isNatList) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(0, z1)) -> a__U41(tt, z1) [0] a__isNatIList(cons(length(z01504), z1)) -> a__U41(a__U11(a__isNatList(z01504)), z1) [0] a__isNatIList(cons(s(z01505), z1)) -> a__U41(a__U21(a__isNat(z01505)), z1) [0] a__isNatIList(cons(z0, z1)) -> a__U41(isNat(z0), z1) [0] a__isNatIList(cons(z0, z1)) -> a__U41(null_a__isNat, z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(0, z1)) -> a__U51(tt, z1) [0] a__isNatList(cons(length(z01506), z1)) -> a__U51(a__U11(a__isNatList(z01506)), z1) [0] a__isNatList(cons(s(z01507), z1)) -> a__U51(a__U21(a__isNat(z01507)), z1) [0] a__isNatList(cons(z0, z1)) -> a__U51(isNat(z0), z1) [0] a__isNatList(cons(z0, z1)) -> a__U51(null_a__isNat, z1) [0] a__isNatList(take(0, z1)) -> a__U61(tt, z1) [0] a__isNatList(take(length(z01508), z1)) -> a__U61(a__U11(a__isNatList(z01508)), z1) [0] a__isNatList(take(s(z01509), z1)) -> a__U61(a__U21(a__isNat(z01509)), z1) [0] a__isNatList(take(z0, z1)) -> a__U61(isNat(z0), z1) [0] a__isNatList(take(z0, z1)) -> a__U61(null_a__isNat, z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, nil)) -> a__U71(tt, nil, z0) [0] a__length(cons(z0, cons(z01510, z1680))) -> a__U71(a__U51(a__isNat(z01510), z1680), cons(z01510, z1680), z0) [0] a__length(cons(z0, take(z01511, z1681))) -> a__U71(a__U61(a__isNat(z01511), z1681), take(z01511, z1681), z0) [0] a__length(cons(z0, z1)) -> a__U71(isNatList(z1), z1, z0) [0] a__length(cons(z0, z1)) -> a__U71(null_a__isNatList, z1, z0) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__U31(a__isNatList(z0))) [0] a__take(0, zeros) -> a__U81(tt) [0] a__take(0, cons(z01512, z1682)) -> a__U81(a__U41(a__isNat(z01512), z1682)) [0] a__take(0, z0) -> a__U81(isNatIList(z0)) [0] a__take(0, z0) -> a__U81(null_a__isNatIList) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__U31(a__isNatList(z2)), z2, z0, z1) [0] a__take(s(z0), cons(z1, zeros)) -> a__U91(tt, zeros, z0, z1) [0] a__take(s(z0), cons(z1, cons(z01513, z1683))) -> a__U91(a__U41(a__isNat(z01513), z1683), cons(z01513, z1683), z0, z1) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(isNatIList(z2), z2, z0, z1) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(null_a__isNatIList, z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0)) -> a__U11(mark(z0)) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0)) -> a__U31(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U42(z0)) -> a__U42(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0)) -> a__U52(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0] mark(U62(z0)) -> a__U62(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1)) -> a__U72(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) [0] mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0) -> null_a__U11 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0) -> null_a__U31 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U42(v0) -> null_a__U42 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0) -> null_a__U52 [0] a__U61(v0, v1) -> null_a__U61 [0] a__U62(v0) -> null_a__U62 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1) -> null_a__U72 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__U92(v0, v1, v2, v3) -> null_a__U92 [0] a__U93(v0, v1, v2, v3) -> null_a__U93 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c20 tt :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c20 :: c22 -> c33:c34 -> c20 A__U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c22 a__isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNAT :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c33:c34 c22 :: c45 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c22 A__LENGTH :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c45 mark :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark MARK :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 A__U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c26 c26 :: c28 -> c33:c34 -> c26 A__U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c28 c28 :: c30 -> c33:c34 -> c28 A__U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c30 c30 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c30 A__ISNATILIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c38:c36 cons :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c38 :: c8 -> c33:c34 -> c38:c36 A__U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c8 A__ISNATLIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c41:c42 c41 :: c12 -> c33:c34 -> c41:c42 A__U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c12 take :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c42 :: c16 -> c33:c34 -> c41:c42 A__U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c16 c45 :: c20 -> c41:c42 -> c45 a__isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark A__TAKE :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c48:c47 s :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c48 :: c26 -> c38:c36 -> c48:c47 a__isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c54 :: c8 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c56 :: c38:c36 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c57 :: c12 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c59 :: c41:c42 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c60 :: c16 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c62 :: c20 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c63 :: c22 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c64 :: c33:c34 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 length :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c65 :: c45 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c67 :: c26 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c68 :: c28 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U93 :: 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c55 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U52 :: 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c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 U81 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_mark :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark const :: c20 const1 :: c22 const2 :: c33:c34 const3 :: c45 const4 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66 const5 :: c26 const6 :: c28 const7 :: c30 const8 :: c38:c36 const9 :: c8 const10 :: c41:c42 const11 :: c12 const12 :: c16 const13 :: c48:c47 Rewrite Strategy: INNERMOST ---------------------------------------- (53) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 2 0 => 0 zeros => 3 nil => 1 null_a__zeros => 0 null_a__U11 => 0 null_a__U21 => 0 null_a__U31 => 0 null_a__U41 => 0 null_a__U42 => 0 null_a__U51 => 0 null_a__U52 => 0 null_a__U61 => 0 null_a__U62 => 0 null_a__U71 => 0 null_a__U72 => 0 null_a__U81 => 0 null_a__U91 => 0 null_a__U92 => 0 null_a__U93 => 0 null_a__isNat => 0 null_a__isNatIList => 0 null_a__isNatList => 0 null_a__length => 0 null_a__take => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 const6 => 0 const7 => 0 const8 => 0 const9 => 0 const10 => 0 const11 => 0 const12 => 0 const13 => 0 ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__U21(a__isNat(z028)), z1) + A__ISNAT(1 + z028) :|: z1 >= 0, z = 1 + (1 + z028) + z1, z028 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__U11(a__isNatList(z027)), z1) + A__ISNAT(1 + z027) :|: z = 1 + (1 + z027) + z1, z1 >= 0, z027 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(2, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__U21(a__isNat(z032)), z1) + A__ISNAT(1 + z032) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__U11(a__isNatList(z031)), z1) + A__ISNAT(1 + z031) :|: z = 1 + (1 + z031) + z1, z031 >= 0, z1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(2, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__U21(a__isNat(z030)), z1) + A__ISNAT(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__U11(a__isNatList(z029)), z1) + A__ISNAT(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(2, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__U61(a__isNat(z034), z110), 1 + z034 + z110, z0) + A__ISNATLIST(1 + z034 + z110) :|: z = 1 + z0 + (1 + z034 + z110), z110 >= 0, z034 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__U51(a__isNat(z033), z19), 1 + z033 + z19, z0) + A__ISNATLIST(1 + z033 + z19) :|: z = 1 + z0 + (1 + z033 + z19), z19 >= 0, z033 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(2, 1, z0) + A__ISNATLIST(1) :|: z0 >= 0, z = 1 + z0 + 1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(0, z1, z0) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(1 + z1, z1, z0) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__U41(a__isNat(z035), z111), 1 + z035 + z111, z0, z1) + A__ISNATILIST(1 + z035 + z111) :|: z1 >= 0, z035 >= 0, z = 1 + z0, z' = 1 + z1 + (1 + z035 + z111), z0 >= 0, z111 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__U31(a__isNatList(z2)), z2, z0, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(2, 3, z0, z1) + A__ISNATILIST(3) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1 + 3 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(0, z2, z0, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(1 + z2, z2, z0, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U41(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U51(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U61(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__U21(a__isNat(z0'')), z0) + A__ISNAT(1 + z0'') :|: z = 2, z'' = 1 + z0'', z0 >= 0, z0'' >= 0, z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__U11(a__isNatList(z0')), z0) + A__ISNAT(1 + z0') :|: z = 2, z0' >= 0, z0 >= 0, z'' = 1 + z0', z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(2, z0) + A__ISNAT(0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(0, z0) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(1 + z1, z0) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U72(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(a__U21(a__isNat(z024)), z0, 1 + z024, z2) + A__ISNAT(1 + z024) :|: z = 2, z024 >= 0, z'' = 1 + z024, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(a__U11(a__isNatList(z023)), z0, 1 + z023, z2) + A__ISNAT(1 + z023) :|: z = 2, z023 >= 0, z'' = 1 + z023, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(2, z0, 0, z2) + A__ISNAT(0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(0, z0, z1, z2) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(1 + z1, z0, z1, z2) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(a__U21(a__isNat(z026)), z0, z1, 1 + z026) + A__ISNAT(1 + z026) :|: z = 2, z1 >= 0, z0 >= 0, z4 = 1 + z026, z026 >= 0, z' = z0, z'' = z1 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(a__U11(a__isNatList(z025)), z0, z1, 1 + z025) + A__ISNAT(1 + z025) :|: z = 2, z025 >= 0, z1 >= 0, z4 = 1 + z025, z0 >= 0, z' = z0, z'' = z1 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(2, z0, z1, 0) + A__ISNAT(0) :|: z = 2, z4 = 0, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(0, z0, z1, z2) + A__ISNAT(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(1 + z2, z0, z1, z2) + A__ISNAT(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U93(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U93(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U92(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U72(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 a__U11(z) -{ 0 }-> 2 :|: z = 2 a__U11(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U11(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z) -{ 0 }-> 2 :|: z = 2 a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z) -{ 0 }-> 2 :|: z = 2 a__U31(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U31(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z, z') -{ 0 }-> a__U42(a__U41(a__isNat(z01466), z1662)) :|: z = 2, z01466 >= 0, z' = 1 + z01466 + z1662, z1662 >= 0 a__U41(z, z') -{ 0 }-> a__U42(a__U31(a__isNatList(z0))) :|: z = 2, z0 >= 0, z' = z0 a__U41(z, z') -{ 0 }-> a__U42(2) :|: z = 2, z' = 3 a__U41(z, z') -{ 0 }-> a__U42(0) :|: z = 2, z0 >= 0, z' = z0 a__U41(z, z') -{ 0 }-> a__U42(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U41(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U41(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U42(z) -{ 0 }-> 2 :|: z = 2 a__U42(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U42(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U61(a__isNat(z01468), z1664)) :|: z = 2, z1664 >= 0, z' = 1 + z01468 + z1664, z01468 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U51(a__isNat(z01467), z1663)) :|: z = 2, z01467 >= 0, z' = 1 + z01467 + z1663, z1663 >= 0 a__U51(z, z') -{ 0 }-> a__U52(2) :|: z = 2, z' = 1 a__U51(z, z') -{ 0 }-> a__U52(0) :|: z = 2, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> a__U52(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U51(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U52(z) -{ 0 }-> 2 :|: z = 2 a__U52(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U52(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U61(z, z') -{ 0 }-> a__U62(a__U41(a__isNat(z01469), z1665)) :|: z = 2, z1665 >= 0, z01469 >= 0, z' = 1 + z01469 + z1665 a__U61(z, z') -{ 0 }-> a__U62(a__U31(a__isNatList(z0))) :|: z = 2, z0 >= 0, z' = z0 a__U61(z, z') -{ 0 }-> a__U62(2) :|: z = 2, z' = 3 a__U61(z, z') -{ 0 }-> a__U62(0) :|: z = 2, z0 >= 0, z' = z0 a__U61(z, z') -{ 0 }-> a__U62(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U61(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U62(z) -{ 0 }-> 2 :|: z = 2 a__U62(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U62(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__U21(a__isNat(z01471)), z0) :|: z = 2, z'' = 1 + z01471, z0 >= 0, z01471 >= 0, z' = z0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__U11(a__isNatList(z01470)), z0) :|: z = 2, z01470 >= 0, z'' = 1 + z01470, z0 >= 0, z' = z0 a__U71(z, z', z'') -{ 0 }-> a__U72(2, z0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0 a__U71(z, z', z'') -{ 0 }-> a__U72(0, z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U71(z, z', z'') -{ 0 }-> a__U72(1 + z1, z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U71(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U71(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U72(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U72(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U72(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(a__U21(a__isNat(z01495)), z0, 1 + z01495, z2) :|: z = 2, z01495 >= 0, z0 >= 0, z'' = 1 + z01495, z' = z0, z2 >= 0, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(a__U11(a__isNatList(z01494)), z0, 1 + z01494, z2) :|: z = 2, z'' = 1 + z01494, z01494 >= 0, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(2, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(0, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(1 + z1, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(a__U21(a__isNat(z01497)), z0, z1, 1 + z01497) :|: z = 2, z1 >= 0, z01497 >= 0, z0 >= 0, z4 = 1 + z01497, z' = z0, z'' = z1 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(a__U11(a__isNatList(z01496)), z0, z1, 1 + z01496) :|: z = 2, z1 >= 0, z01496 >= 0, z0 >= 0, z' = z0, z'' = z1, z4 = 1 + z01496 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(2, z0, z1, 0) :|: z = 2, z4 = 0, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(0, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(1 + z2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U92(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U93(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U21(a__isNat(z01501))) :|: z01501 >= 0, z = 1 + (1 + z01501) a__isNat(z) -{ 0 }-> a__U21(a__U11(a__isNatList(z01500))) :|: z = 1 + (1 + z01500), z01500 >= 0 a__isNat(z) -{ 0 }-> a__U21(2) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U61(a__isNat(z01499), z1677)) :|: z1677 >= 0, z = 1 + (1 + z01499 + z1677), z01499 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U51(a__isNat(z01498), z1676)) :|: z = 1 + (1 + z01498 + z1676), z01498 >= 0, z1676 >= 0 a__isNat(z) -{ 0 }-> a__U11(2) :|: z = 1 + 1 a__isNat(z) -{ 0 }-> a__U11(0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(1 + z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__U21(a__isNat(z01505)), z1) :|: z1 >= 0, z01505 >= 0, z = 1 + (1 + z01505) + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__U11(a__isNatList(z01504)), z1) :|: z1 >= 0, z = 1 + (1 + z01504) + z1, z01504 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(2, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__U61(a__isNat(z01503), z1679)) :|: z01503 >= 0, z1679 >= 0, z = 1 + z01503 + z1679 a__isNatIList(z) -{ 0 }-> a__U31(a__U51(a__isNat(z01502), z1678)) :|: z = 1 + z01502 + z1678, z1678 >= 0, z01502 >= 0 a__isNatIList(z) -{ 0 }-> a__U31(2) :|: z = 1 a__isNatIList(z) -{ 0 }-> a__U31(0) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U31(1 + z0) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__U21(a__isNat(z01509)), z1) :|: z1 >= 0, z = 1 + (1 + z01509) + z1, z01509 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__U11(a__isNatList(z01508)), z1) :|: z1 >= 0, z01508 >= 0, z = 1 + (1 + z01508) + z1 a__isNatList(z) -{ 0 }-> a__U61(2, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U61(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U61(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__U21(a__isNat(z01507)), z1) :|: z1 >= 0, z01507 >= 0, z = 1 + (1 + z01507) + z1 a__isNatList(z) -{ 0 }-> a__U51(a__U11(a__isNatList(z01506)), z1) :|: z1 >= 0, z01506 >= 0, z = 1 + (1 + z01506) + z1 a__isNatList(z) -{ 0 }-> a__U51(2, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U51(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> a__U71(a__U61(a__isNat(z01511), z1681), 1 + z01511 + z1681, z0) :|: z1681 >= 0, z0 >= 0, z = 1 + z0 + (1 + z01511 + z1681), z01511 >= 0 a__length(z) -{ 0 }-> a__U71(a__U51(a__isNat(z01510), z1680), 1 + z01510 + z1680, z0) :|: z01510 >= 0, z1680 >= 0, z0 >= 0, z = 1 + z0 + (1 + z01510 + z1680) a__length(z) -{ 0 }-> a__U71(2, 1, z0) :|: z0 >= 0, z = 1 + z0 + 1 a__length(z) -{ 0 }-> a__U71(0, z1, z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> a__U71(1 + z1, z1, z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__U41(a__isNat(z01513), z1683), 1 + z01513 + z1683, z0, z1) :|: z1 >= 0, z01513 >= 0, z = 1 + z0, z1683 >= 0, z0 >= 0, z' = 1 + z1 + (1 + z01513 + z1683) a__take(z, z') -{ 0 }-> a__U91(a__U31(a__isNatList(z2)), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(2, 3, z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1 + 3 a__take(z, z') -{ 0 }-> a__U91(0, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(1 + z2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__U41(a__isNat(z01512), z1682)) :|: z' = 1 + z01512 + z1682, z1682 >= 0, z = 0, z01512 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__U31(a__isNatList(z0))) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> a__U81(2) :|: z' = 3, z = 0 a__take(z, z') -{ 0 }-> a__U81(0) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> a__U81(1 + z0) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__zeros :|: z = 3 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U93(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U92(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U72(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U71(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U52(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U42(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U41(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U31(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (55) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: a__U11(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U11(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U11(z) -{ 0 }-> 2 :|: z = 2 a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z) -{ 0 }-> 2 :|: z = 2 a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U31(z) -{ 0 }-> 2 :|: z = 2 a__U31(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U31(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U42(z) -{ 0 }-> 2 :|: z = 2 a__U42(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U42(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U52(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U52(z) -{ 0 }-> 2 :|: z = 2 a__U52(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U62(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U62(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U62(z) -{ 0 }-> 2 :|: z = 2 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 :|: z = 2 ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__U21(a__isNat(z028)), z1) + A__ISNAT(1 + z028) :|: z1 >= 0, z = 1 + (1 + z028) + z1, z028 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__U11(a__isNatList(z027)), z1) + A__ISNAT(1 + z027) :|: z = 1 + (1 + z027) + z1, z1 >= 0, z027 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(2, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__U21(a__isNat(z032)), z1) + A__ISNAT(1 + z032) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__U11(a__isNatList(z031)), z1) + A__ISNAT(1 + z031) :|: z = 1 + (1 + z031) + z1, z031 >= 0, z1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(2, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__U21(a__isNat(z030)), z1) + A__ISNAT(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__U11(a__isNatList(z029)), z1) + A__ISNAT(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(2, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__U61(a__isNat(z034), z110), 1 + z034 + z110, z0) + A__ISNATLIST(1 + z034 + z110) :|: z = 1 + z0 + (1 + z034 + z110), z110 >= 0, z034 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__U51(a__isNat(z033), z19), 1 + z033 + z19, z0) + A__ISNATLIST(1 + z033 + z19) :|: z = 1 + z0 + (1 + z033 + z19), z19 >= 0, z033 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(2, 1, z0) + A__ISNATLIST(1) :|: z0 >= 0, z = 1 + z0 + 1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(0, z1, z0) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(1 + z1, z1, z0) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__U41(a__isNat(z035), z111), 1 + z035 + z111, z0, z1) + A__ISNATILIST(1 + z035 + z111) :|: z1 >= 0, z035 >= 0, z = 1 + z0, z' = 1 + z1 + (1 + z035 + z111), z0 >= 0, z111 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__U31(a__isNatList(z2)), z2, z0, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(2, 3, z0, z1) + A__ISNATILIST(3) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1 + 3 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(0, z2, z0, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(1 + z2, z2, z0, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U41(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U51(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U61(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__U21(a__isNat(z0'')), z0) + A__ISNAT(1 + z0'') :|: z = 2, z'' = 1 + z0'', z0 >= 0, z0'' >= 0, z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__U11(a__isNatList(z0')), z0) + A__ISNAT(1 + z0') :|: z = 2, z0' >= 0, z0 >= 0, z'' = 1 + z0', z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(2, z0) + A__ISNAT(0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(0, z0) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(1 + z1, z0) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U72(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(a__U21(a__isNat(z024)), z0, 1 + z024, z2) + A__ISNAT(1 + z024) :|: z = 2, z024 >= 0, z'' = 1 + z024, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(a__U11(a__isNatList(z023)), z0, 1 + z023, z2) + A__ISNAT(1 + z023) :|: z = 2, z023 >= 0, z'' = 1 + z023, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(2, z0, 0, z2) + A__ISNAT(0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(0, z0, z1, z2) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(1 + z1, z0, z1, z2) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(a__U21(a__isNat(z026)), z0, z1, 1 + z026) + A__ISNAT(1 + z026) :|: z = 2, z1 >= 0, z0 >= 0, z4 = 1 + z026, z026 >= 0, z' = z0, z'' = z1 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(a__U11(a__isNatList(z025)), z0, z1, 1 + z025) + A__ISNAT(1 + z025) :|: z = 2, z025 >= 0, z1 >= 0, z4 = 1 + z025, z0 >= 0, z' = z0, z'' = z1 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(2, z0, z1, 0) + A__ISNAT(0) :|: z = 2, z4 = 0, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(0, z0, z1, z2) + A__ISNAT(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(1 + z2, z0, z1, z2) + A__ISNAT(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U93(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U93(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U92(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U72(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 a__U11(z) -{ 0 }-> 2 :|: z = 2 a__U11(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U11(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z) -{ 0 }-> 2 :|: z = 2 a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z) -{ 0 }-> 2 :|: z = 2 a__U31(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U31(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z, z') -{ 0 }-> a__U42(a__U41(a__isNat(z01466), z1662)) :|: z = 2, z01466 >= 0, z' = 1 + z01466 + z1662, z1662 >= 0 a__U41(z, z') -{ 0 }-> a__U42(a__U31(a__isNatList(z0))) :|: z = 2, z0 >= 0, z' = z0 a__U41(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U41(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U41(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U41(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U41(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U41(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U41(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U41(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U41(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U41(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U42(z) -{ 0 }-> 2 :|: z = 2 a__U42(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U42(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U61(a__isNat(z01468), z1664)) :|: z = 2, z1664 >= 0, z' = 1 + z01468 + z1664, z01468 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U51(a__isNat(z01467), z1663)) :|: z = 2, z01467 >= 0, z' = 1 + z01467 + z1663, z1663 >= 0 a__U51(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U51(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U51(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U51(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U51(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U51(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U51(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U51(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U52(z) -{ 0 }-> 2 :|: z = 2 a__U52(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U52(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U61(z, z') -{ 0 }-> a__U62(a__U41(a__isNat(z01469), z1665)) :|: z = 2, z1665 >= 0, z01469 >= 0, z' = 1 + z01469 + z1665 a__U61(z, z') -{ 0 }-> a__U62(a__U31(a__isNatList(z0))) :|: z = 2, z0 >= 0, z' = z0 a__U61(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U61(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U61(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U61(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U61(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U61(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U61(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U61(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U61(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U62(z) -{ 0 }-> 2 :|: z = 2 a__U62(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U62(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__U21(a__isNat(z01471)), z0) :|: z = 2, z'' = 1 + z01471, z0 >= 0, z01471 >= 0, z' = z0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__U11(a__isNatList(z01470)), z0) :|: z = 2, z01470 >= 0, z'' = 1 + z01470, z0 >= 0, z' = z0 a__U71(z, z', z'') -{ 0 }-> a__U72(2, z0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0 a__U71(z, z', z'') -{ 0 }-> a__U72(0, z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U71(z, z', z'') -{ 0 }-> a__U72(1 + z1, z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U71(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U71(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U72(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U72(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U72(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(a__U21(a__isNat(z01495)), z0, 1 + z01495, z2) :|: z = 2, z01495 >= 0, z0 >= 0, z'' = 1 + z01495, z' = z0, z2 >= 0, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(a__U11(a__isNatList(z01494)), z0, 1 + z01494, z2) :|: z = 2, z'' = 1 + z01494, z01494 >= 0, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(2, z0, 0, z2) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, z2 >= 0, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(0, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(1 + z1, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(a__U21(a__isNat(z01497)), z0, z1, 1 + z01497) :|: z = 2, z1 >= 0, z01497 >= 0, z0 >= 0, z4 = 1 + z01497, z' = z0, z'' = z1 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(a__U11(a__isNatList(z01496)), z0, z1, 1 + z01496) :|: z = 2, z1 >= 0, z01496 >= 0, z0 >= 0, z' = z0, z'' = z1, z4 = 1 + z01496 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(2, z0, z1, 0) :|: z = 2, z4 = 0, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(0, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(1 + z2, z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U92(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U93(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U21(a__isNat(z01501))) :|: z01501 >= 0, z = 1 + (1 + z01501) a__isNat(z) -{ 0 }-> a__U21(a__U11(a__isNatList(z01500))) :|: z = 1 + (1 + z01500), z01500 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U61(a__isNat(z01499), z1677)) :|: z1677 >= 0, z = 1 + (1 + z01499 + z1677), z01499 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U51(a__isNat(z01498), z1676)) :|: z = 1 + (1 + z01498 + z1676), z01498 >= 0, z1676 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 2 :|: z = 1 + 1, 2 = 2 a__isNat(z) -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, 1 + z0 = 2 a__isNat(z) -{ 0 }-> 2 :|: z = 1 + 0, 2 = 2 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 2 = v0 a__isNat(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 1 + z0 = v0 a__isNat(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0 a__isNat(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 2 = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 2 = z0, z0 >= 0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 2 = z0, z0 >= 0 a__isNat(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 1 + z0 = z0', z0' >= 0 a__isNat(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__U21(a__isNat(z01505)), z1) :|: z1 >= 0, z01505 >= 0, z = 1 + (1 + z01505) + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__U11(a__isNatList(z01504)), z1) :|: z1 >= 0, z = 1 + (1 + z01504) + z1, z01504 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(2, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__U61(a__isNat(z01503), z1679)) :|: z01503 >= 0, z1679 >= 0, z = 1 + z01503 + z1679 a__isNatIList(z) -{ 0 }-> a__U31(a__U51(a__isNat(z01502), z1678)) :|: z = 1 + z01502 + z1678, z1678 >= 0, z01502 >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 2 :|: z = 1, 2 = 2 a__isNatIList(z) -{ 0 }-> 2 :|: z = z0, z0 >= 0, 1 + z0 = 2 a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIList(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 2 = v0 a__isNatIList(z) -{ 0 }-> 0 :|: z = z0, z0 >= 0, v0 >= 0, 1 + z0 = v0 a__isNatIList(z) -{ 0 }-> 0 :|: z = z0, z0 >= 0, v0 >= 0, 0 = v0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = 1, 2 = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 1 + z0' :|: z = z0, z0 >= 0, 1 + z0 = z0', z0' >= 0 a__isNatIList(z) -{ 0 }-> 1 + z0' :|: z = z0, z0 >= 0, 0 = z0', z0' >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__U21(a__isNat(z01509)), z1) :|: z1 >= 0, z = 1 + (1 + z01509) + z1, z01509 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__U11(a__isNatList(z01508)), z1) :|: z1 >= 0, z01508 >= 0, z = 1 + (1 + z01508) + z1 a__isNatList(z) -{ 0 }-> a__U61(2, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U61(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U61(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__U21(a__isNat(z01507)), z1) :|: z1 >= 0, z01507 >= 0, z = 1 + (1 + z01507) + z1 a__isNatList(z) -{ 0 }-> a__U51(a__U11(a__isNatList(z01506)), z1) :|: z1 >= 0, z01506 >= 0, z = 1 + (1 + z01506) + z1 a__isNatList(z) -{ 0 }-> a__U51(2, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U51(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> a__U71(a__U61(a__isNat(z01511), z1681), 1 + z01511 + z1681, z0) :|: z1681 >= 0, z0 >= 0, z = 1 + z0 + (1 + z01511 + z1681), z01511 >= 0 a__length(z) -{ 0 }-> a__U71(a__U51(a__isNat(z01510), z1680), 1 + z01510 + z1680, z0) :|: z01510 >= 0, z1680 >= 0, z0 >= 0, z = 1 + z0 + (1 + z01510 + z1680) a__length(z) -{ 0 }-> a__U71(2, 1, z0) :|: z0 >= 0, z = 1 + z0 + 1 a__length(z) -{ 0 }-> a__U71(0, z1, z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> a__U71(1 + z1, z1, z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__U41(a__isNat(z01513), z1683), 1 + z01513 + z1683, z0, z1) :|: z1 >= 0, z01513 >= 0, z = 1 + z0, z1683 >= 0, z0 >= 0, z' = 1 + z1 + (1 + z01513 + z1683) a__take(z, z') -{ 0 }-> a__U91(a__U31(a__isNatList(z2)), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(2, 3, z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1 + 3 a__take(z, z') -{ 0 }-> a__U91(0, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(1 + z2, z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__U41(a__isNat(z01512), z1682)) :|: z' = 1 + z01512 + z1682, z1682 >= 0, z = 0, z01512 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__U31(a__isNatList(z0))) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 1 :|: z' = 3, z = 0, 2 = 2 a__take(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0, 1 + z0 = 2 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 0 :|: z' = 3, z = 0, v0 >= 0, 2 = v0 a__take(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__take(z, z') -{ 0 }-> 0 :|: z0 >= 0, z = 0, z' = z0, v0 >= 0, 0 = v0 a__take(z, z') -{ 0 }-> 1 + z0 :|: z' = 3, z = 0, 2 = z0, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + z0' :|: z0 >= 0, z = 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__take(z, z') -{ 0 }-> 1 + z0' :|: z0 >= 0, z = 0, z' = z0, 0 = z0', z0' >= 0 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U93(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U92(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U72(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U71(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U52(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U42(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U41(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U31(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (57) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 1 }-> 1 + A__ISNATLIST(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__ISNATLIST(z) :|: z >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__U21(a__isNat(z028)), z1) + A__ISNAT(1 + z028) :|: z1 >= 0, z = 1 + (1 + z028) + z1, z028 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__U11(a__isNatList(z027)), z1) + A__ISNAT(1 + z027) :|: z = 1 + (1 + z027) + z1, z1 >= 0, z027 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(2, z - 1) + A__ISNAT(0) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__U21(a__isNat(z032)), z1) + A__ISNAT(1 + z032) :|: z032 >= 0, z1 >= 0, z = 1 + (1 + z032) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__U11(a__isNatList(z031)), z1) + A__ISNAT(1 + z031) :|: z = 1 + (1 + z031) + z1, z031 >= 0, z1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(2, z - 1) + A__ISNAT(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__U21(a__isNat(z030)), z1) + A__ISNAT(1 + z030) :|: z1 >= 0, z = 1 + (1 + z030) + z1, z030 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__U11(a__isNatList(z029)), z1) + A__ISNAT(1 + z029) :|: z029 >= 0, z = 1 + (1 + z029) + z1, z1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(2, z - 1) + A__ISNAT(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__U61(a__isNat(z034), z110), 1 + z034 + z110, z0) + A__ISNATLIST(1 + z034 + z110) :|: z = 1 + z0 + (1 + z034 + z110), z110 >= 0, z034 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__U51(a__isNat(z033), z19), 1 + z033 + z19, z0) + A__ISNATLIST(1 + z033 + z19) :|: z = 1 + z0 + (1 + z033 + z19), z19 >= 0, z033 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(2, 1, z - 2) + A__ISNATLIST(1) :|: z - 2 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(0, z1, z0) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__U71(1 + z1, z1, z0) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__ISNATILIST(z') :|: z' >= 0, z = 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__U41(a__isNat(z035), z111), 1 + z035 + z111, z - 1, z1) + A__ISNATILIST(1 + z035 + z111) :|: z1 >= 0, z035 >= 0, z' = 1 + z1 + (1 + z035 + z111), z - 1 >= 0, z111 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__U31(a__isNatList(z2)), z2, z - 1, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(2, 3, z - 1, z' - 4) + A__ISNATILIST(3) :|: z' - 4 >= 0, z - 1 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(0, z2, z - 1, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(1 + z2, z2, z - 1, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__U41(z, z') -{ 1 }-> 1 + A__ISNATILIST(z') :|: z = 2, z' >= 0 A__U51(z, z') -{ 1 }-> 1 + A__ISNATLIST(z') :|: z = 2, z' >= 0 A__U61(z, z') -{ 1 }-> 1 + A__ISNATILIST(z') :|: z = 2, z' >= 0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__U21(a__isNat(z'' - 1)), z') + A__ISNAT(1 + (z'' - 1)) :|: z = 2, z' >= 0, z'' - 1 >= 0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__U11(a__isNatList(z'' - 1)), z') + A__ISNAT(1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(2, z') + A__ISNAT(0) :|: z = 2, z'' = 0, z' >= 0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(0, z') + A__ISNAT(z'') :|: z = 2, z'' >= 0, z' >= 0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(1 + z'', z') + A__ISNAT(z'') :|: z = 2, z'' >= 0, z' >= 0 A__U72(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z')) + MARK(z') :|: z = 2, z' >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1), z4) + A__ISNAT(1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z4 >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(a__U11(a__isNatList(z'' - 1)), z', 1 + (z'' - 1), z4) + A__ISNAT(1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z4 >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(2, z', 0, z4) + A__ISNAT(0) :|: z = 2, z'' = 0, z' >= 0, z4 >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(0, z', z'', z4) + A__ISNAT(z'') :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(1 + z'', z', z'', z4) + A__ISNAT(z'') :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(a__U21(a__isNat(z4 - 1)), z', z'', 1 + (z4 - 1)) + A__ISNAT(1 + (z4 - 1)) :|: z = 2, z'' >= 0, z' >= 0, z4 - 1 >= 0 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(a__U11(a__isNatList(z4 - 1)), z', z'', 1 + (z4 - 1)) + A__ISNAT(1 + (z4 - 1)) :|: z = 2, z4 - 1 >= 0, z'' >= 0, z' >= 0 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(2, z', z'', 0) + A__ISNAT(0) :|: z = 2, z4 = 0, z'' >= 0, z' >= 0 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(0, z', z'', z4) + A__ISNAT(z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(1 + z4, z', z'', z4) + A__ISNAT(z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 A__U93(z, z', z'', z4) -{ 1 }-> 1 + MARK(z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U93(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U92(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U72(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z - 1)) + MARK(z - 1) :|: z - 1 >= 0 a__U11(z) -{ 0 }-> 2 :|: z = 2 a__U11(z) -{ 0 }-> 0 :|: z >= 0 a__U11(z) -{ 0 }-> 1 + z :|: z >= 0 a__U21(z) -{ 0 }-> 2 :|: z = 2 a__U21(z) -{ 0 }-> 0 :|: z >= 0 a__U21(z) -{ 0 }-> 1 + z :|: z >= 0 a__U31(z) -{ 0 }-> 2 :|: z = 2 a__U31(z) -{ 0 }-> 0 :|: z >= 0 a__U31(z) -{ 0 }-> 1 + z :|: z >= 0 a__U41(z, z') -{ 0 }-> a__U42(a__U41(a__isNat(z01466), z1662)) :|: z = 2, z01466 >= 0, z' = 1 + z01466 + z1662, z1662 >= 0 a__U41(z, z') -{ 0 }-> a__U42(a__U31(a__isNatList(z'))) :|: z = 2, z' >= 0 a__U41(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U41(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U41(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U41(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U41(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U41(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U41(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U41(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U41(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U41(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U42(z) -{ 0 }-> 2 :|: z = 2 a__U42(z) -{ 0 }-> 0 :|: z >= 0 a__U42(z) -{ 0 }-> 1 + z :|: z >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U61(a__isNat(z01468), z1664)) :|: z = 2, z1664 >= 0, z' = 1 + z01468 + z1664, z01468 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__U51(a__isNat(z01467), z1663)) :|: z = 2, z01467 >= 0, z' = 1 + z01467 + z1663, z1663 >= 0 a__U51(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U51(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U51(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U51(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U51(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U51(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U51(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U51(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U51(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U52(z) -{ 0 }-> 2 :|: z = 2 a__U52(z) -{ 0 }-> 0 :|: z >= 0 a__U52(z) -{ 0 }-> 1 + z :|: z >= 0 a__U61(z, z') -{ 0 }-> a__U62(a__U41(a__isNat(z01469), z1665)) :|: z = 2, z1665 >= 0, z01469 >= 0, z' = 1 + z01469 + z1665 a__U61(z, z') -{ 0 }-> a__U62(a__U31(a__isNatList(z'))) :|: z = 2, z' >= 0 a__U61(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U61(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U61(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U61(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U61(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U61(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U61(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U61(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U61(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U61(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U62(z) -{ 0 }-> 2 :|: z = 2 a__U62(z) -{ 0 }-> 0 :|: z >= 0 a__U62(z) -{ 0 }-> 1 + z :|: z >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__U21(a__isNat(z'' - 1)), z') :|: z = 2, z' >= 0, z'' - 1 >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__U11(a__isNatList(z'' - 1)), z') :|: z = 2, z'' - 1 >= 0, z' >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(2, z') :|: z = 2, z'' = 0, z' >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(0, z') :|: z = 2, z'' >= 0, z' >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(1 + z'', z') :|: z = 2, z'' >= 0, z' >= 0 a__U71(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U71(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U72(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U72(z, z') -{ 0 }-> 1 + a__length(mark(z')) :|: z = 2, z' >= 0 a__U72(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: z >= 0 a__U81(z) -{ 0 }-> 1 + z :|: z >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1), z4) :|: z = 2, z'' - 1 >= 0, z' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(a__U11(a__isNatList(z'' - 1)), z', 1 + (z'' - 1), z4) :|: z = 2, z'' - 1 >= 0, z' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(2, z', 0, z4) :|: z = 2, z'' = 0, z' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(0, z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(1 + z'', z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z + z' + z'' + z4 :|: z' >= 0, z >= 0, z'' >= 0, z4 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(a__U21(a__isNat(z4 - 1)), z', z'', 1 + (z4 - 1)) :|: z = 2, z'' >= 0, z4 - 1 >= 0, z' >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(a__U11(a__isNatList(z4 - 1)), z', z'', 1 + (z4 - 1)) :|: z = 2, z'' >= 0, z4 - 1 >= 0, z' >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(2, z', z'', 0) :|: z = 2, z4 = 0, z'' >= 0, z' >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(0, z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(1 + z4, z', z'', z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z4 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> 1 + z + z' + z'' + z4 :|: z' >= 0, z >= 0, z'' >= 0, z4 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z4 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 1 + mark(z4) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 1 + z + z' + z'' + z4 :|: z' >= 0, z >= 0, z'' >= 0, z4 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U21(a__isNat(z - 2))) :|: z - 2 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__U11(a__isNatList(z - 2))) :|: z - 2 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U61(a__isNat(z01499), z1677)) :|: z1677 >= 0, z = 1 + (1 + z01499 + z1677), z01499 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__U51(a__isNat(z01498), z1676)) :|: z = 1 + (1 + z01498 + z1676), z01498 >= 0, z1676 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 2 :|: z = 1 + 1, 2 = 2 a__isNat(z) -{ 0 }-> 2 :|: z - 1 >= 0, 1 + (z - 1) = 2 a__isNat(z) -{ 0 }-> 2 :|: z = 1 + 0, 2 = 2 a__isNat(z) -{ 0 }-> 0 :|: z >= 0 a__isNat(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 2 = v0 a__isNat(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 1 + (z - 1) = v0 a__isNat(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0 a__isNat(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 2 = v0 a__isNat(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 2 = z0, z0 >= 0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 2 = z0, z0 >= 0 a__isNat(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 1 + (z - 1) = z0', z0' >= 0 a__isNat(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__U21(a__isNat(z01505)), z1) :|: z1 >= 0, z01505 >= 0, z = 1 + (1 + z01505) + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__U11(a__isNatList(z01504)), z1) :|: z1 >= 0, z = 1 + (1 + z01504) + z1, z01504 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(2, z - 1) :|: z - 1 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__U61(a__isNat(z01503), z1679)) :|: z01503 >= 0, z1679 >= 0, z = 1 + z01503 + z1679 a__isNatIList(z) -{ 0 }-> a__U31(a__U51(a__isNat(z01502), z1678)) :|: z = 1 + z01502 + z1678, z1678 >= 0, z01502 >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 2 :|: z = 1, 2 = 2 a__isNatIList(z) -{ 0 }-> 2 :|: z >= 0, 1 + z = 2 a__isNatIList(z) -{ 0 }-> 0 :|: z >= 0 a__isNatIList(z) -{ 0 }-> 0 :|: z = 1, v0 >= 0, 2 = v0 a__isNatIList(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 1 + z = v0 a__isNatIList(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0 a__isNatIList(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = 1, 2 = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 1 + z0' :|: z >= 0, 1 + z = z0', z0' >= 0 a__isNatIList(z) -{ 0 }-> 1 + z0' :|: z >= 0, 0 = z0', z0' >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__U21(a__isNat(z01509)), z1) :|: z1 >= 0, z = 1 + (1 + z01509) + z1, z01509 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__U11(a__isNatList(z01508)), z1) :|: z1 >= 0, z01508 >= 0, z = 1 + (1 + z01508) + z1 a__isNatList(z) -{ 0 }-> a__U61(2, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 0 }-> a__U61(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U61(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__U21(a__isNat(z01507)), z1) :|: z1 >= 0, z01507 >= 0, z = 1 + (1 + z01507) + z1 a__isNatList(z) -{ 0 }-> a__U51(a__U11(a__isNatList(z01506)), z1) :|: z1 >= 0, z01506 >= 0, z = 1 + (1 + z01506) + z1 a__isNatList(z) -{ 0 }-> a__U51(2, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 0 }-> a__U51(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: z >= 0 a__isNatList(z) -{ 0 }-> 1 + z :|: z >= 0 a__length(z) -{ 0 }-> a__U71(a__U61(a__isNat(z01511), z1681), 1 + z01511 + z1681, z0) :|: z1681 >= 0, z0 >= 0, z = 1 + z0 + (1 + z01511 + z1681), z01511 >= 0 a__length(z) -{ 0 }-> a__U71(a__U51(a__isNat(z01510), z1680), 1 + z01510 + z1680, z0) :|: z01510 >= 0, z1680 >= 0, z0 >= 0, z = 1 + z0 + (1 + z01510 + z1680) a__length(z) -{ 0 }-> a__U71(2, 1, z - 2) :|: z - 2 >= 0 a__length(z) -{ 0 }-> a__U71(0, z1, z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> a__U71(1 + z1, z1, z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: z >= 0 a__length(z) -{ 0 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 0 }-> a__U91(a__U41(a__isNat(z01513), z1683), 1 + z01513 + z1683, z - 1, z1) :|: z1 >= 0, z01513 >= 0, z1683 >= 0, z - 1 >= 0, z' = 1 + z1 + (1 + z01513 + z1683) a__take(z, z') -{ 0 }-> a__U91(a__U31(a__isNatList(z2)), z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(2, 3, z - 1, z' - 4) :|: z' - 4 >= 0, z - 1 >= 0 a__take(z, z') -{ 0 }-> a__U91(0, z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(1 + z2, z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__U41(a__isNat(z01512), z1682)) :|: z' = 1 + z01512 + z1682, z1682 >= 0, z = 0, z01512 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__U31(a__isNatList(z'))) :|: z' >= 0, z = 0 a__take(z, z') -{ 0 }-> 1 :|: z' = 3, z = 0, 2 = 2 a__take(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0, 1 + z' = 2 a__take(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__take(z, z') -{ 0 }-> 0 :|: z' = 3, z = 0, v0 >= 0, 2 = v0 a__take(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0, v0 >= 0, 1 + z' = v0 a__take(z, z') -{ 0 }-> 0 :|: z' >= 0, z = 0, v0 >= 0, 0 = v0 a__take(z, z') -{ 0 }-> 1 + z0 :|: z' = 3, z = 0, 2 = z0, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + z0' :|: z' >= 0, z = 0, 1 + z' = z0', z0' >= 0 a__take(z, z') -{ 0 }-> 1 + z0' :|: z' >= 0, z = 0, 0 = z0', z0' >= 0 a__take(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNatList(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNatIList(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U93(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U92(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U72(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U71(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U52(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U42(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U41(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U31(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U21(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U11(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (59) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__zeros -> null_a__zeros [0] a__U11(v0) -> null_a__U11 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0) -> null_a__U31 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U42(v0) -> null_a__U42 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0) -> null_a__U52 [0] a__U61(v0, v1) -> null_a__U61 [0] a__U62(v0) -> null_a__U62 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1) -> null_a__U72 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__U92(v0, v1, v2, v3) -> null_a__U92 [0] a__U93(v0, v1, v2, v3) -> null_a__U93 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__U71(v0, v1, v2) -> null_A__U71 [0] A__U72(v0, v1) -> null_A__U72 [0] A__U91(v0, v1, v2, v3) -> null_A__U91 [0] A__U92(v0, v1, v2, v3) -> null_A__U92 [0] A__U93(v0, v1, v2, v3) -> null_A__U93 [0] A__ISNATLIST(v0) -> null_A__ISNATLIST [0] A__LENGTH(v0) -> null_A__LENGTH [0] A__TAKE(v0, v1) -> null_A__TAKE [0] MARK(v0) -> null_MARK [0] A__U41(v0, v1) -> null_A__U41 [0] A__U51(v0, v1) -> null_A__U51 [0] A__U61(v0, v1) -> null_A__U61 [0] A__ISNAT(v0) -> null_A__ISNAT [0] And the following fresh constants: null_a__zeros, null_a__U11, null_a__U21, null_a__U31, null_a__U41, null_a__U42, null_a__U51, null_a__U52, null_a__U61, null_a__U62, null_a__U71, null_a__U72, null_a__U81, null_a__U91, null_a__U92, null_a__U93, null_a__isNat, null_a__isNatIList, null_a__isNatList, null_a__length, null_a__take, null_mark, null_A__U71, null_A__U72, null_A__U91, null_A__U92, null_A__U93, null_A__ISNATLIST, null_A__LENGTH, null_A__TAKE, null_MARK, null_A__U41, null_A__U51, null_A__U61, null_A__ISNAT, const ---------------------------------------- (60) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) [1] A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) [1] A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) [1] A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) [1] A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) [1] MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) [1] MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c64(A__ISNAT(z0)) [1] MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c72(MARK(z0)) [1] MARK(s(z0)) -> c75(MARK(z0)) [1] A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) [1] A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) [1] A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) [1] A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) [1] A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) [1] A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) [1] MARK(U11(z0)) -> c51(MARK(z0)) [1] MARK(U21(z0)) -> c52(MARK(z0)) [1] MARK(U31(z0)) -> c53(MARK(z0)) [1] MARK(U42(z0)) -> c55(MARK(z0)) [1] MARK(U52(z0)) -> c58(MARK(z0)) [1] MARK(U62(z0)) -> c61(MARK(z0)) [1] MARK(U81(z0)) -> c66(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt) -> tt [0] a__U11(z0) -> U11(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt) -> tt [0] a__U31(z0) -> U31(z0) [0] a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U42(tt) -> tt [0] a__U42(z0) -> U42(z0) [0] a__U51(tt, z0) -> a__U52(a__isNatList(z0)) [0] a__U51(z0, z1) -> U51(z0, z1) [0] a__U52(tt) -> tt [0] a__U52(z0) -> U52(z0) [0] a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) [0] a__U61(z0, z1) -> U61(z0, z1) [0] a__U62(tt) -> tt [0] a__U62(z0) -> U62(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0) -> s(a__length(mark(z0))) [0] a__U72(z0, z1) -> U72(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) [0] a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) [0] a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatList(z0)) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__isNatIList(z0)) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0)) -> a__U11(mark(z0)) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0)) -> a__U31(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U42(z0)) -> a__U42(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1)) -> a__U51(mark(z0), z1) [0] mark(U52(z0)) -> a__U52(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U61(z0, z1)) -> a__U61(mark(z0), z1) [0] mark(U62(z0)) -> a__U62(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1)) -> a__U72(mark(z0), z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) [0] mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0) -> null_a__U11 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0) -> null_a__U31 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U42(v0) -> null_a__U42 [0] a__U51(v0, v1) -> null_a__U51 [0] a__U52(v0) -> null_a__U52 [0] a__U61(v0, v1) -> null_a__U61 [0] a__U62(v0) -> null_a__U62 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1) -> null_a__U72 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__U92(v0, v1, v2, v3) -> null_a__U92 [0] a__U93(v0, v1, v2, v3) -> null_a__U93 [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__U71(v0, v1, v2) -> null_A__U71 [0] A__U72(v0, v1) -> null_A__U72 [0] A__U91(v0, v1, v2, v3) -> null_A__U91 [0] A__U92(v0, v1, v2, v3) -> null_A__U92 [0] A__U93(v0, v1, v2, v3) -> null_A__U93 [0] A__ISNATLIST(v0) -> null_A__ISNATLIST [0] A__LENGTH(v0) -> null_A__LENGTH [0] A__TAKE(v0, v1) -> null_A__TAKE [0] MARK(v0) -> null_MARK [0] A__U41(v0, v1) -> null_A__U41 [0] A__U51(v0, v1) -> null_A__U51 [0] A__U61(v0, v1) -> null_A__U61 [0] A__ISNAT(v0) -> null_A__ISNAT [0] The TRS has the following type information: A__U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c20:null_A__U71 tt :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c20 :: c22:null_A__U72 -> c33:c34:null_A__ISNAT -> c20:null_A__U71 A__U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c22:null_A__U72 a__isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNAT :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c33:c34:null_A__ISNAT c22 :: c45:null_A__LENGTH -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c22:null_A__U72 A__LENGTH :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c45:null_A__LENGTH mark :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark MARK :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK A__U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c26:null_A__U91 c26 :: c28:null_A__U92 -> c33:c34:null_A__ISNAT -> c26:null_A__U91 A__U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c28:null_A__U92 c28 :: c30:null_A__U93 -> c33:c34:null_A__ISNAT -> c28:null_A__U92 A__U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c30:null_A__U93 c30 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c30:null_A__U93 A__ISNATILIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c38:c36 cons :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c38 :: c8:null_A__U41 -> c33:c34:null_A__ISNAT -> c38:c36 A__U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c8:null_A__U41 A__ISNATLIST :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c41:c42:null_A__ISNATLIST c41 :: c12:null_A__U51 -> c33:c34:null_A__ISNAT -> c41:c42:null_A__ISNATLIST A__U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c12:null_A__U51 take :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c42 :: c16:null_A__U61 -> c33:c34:null_A__ISNAT -> c41:c42:null_A__ISNATLIST A__U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c16:null_A__U61 c45 :: c20:null_A__U71 -> c41:c42:null_A__ISNATLIST -> c45:null_A__LENGTH a__isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark A__TAKE :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> c48:c47:null_A__TAKE s :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c48 :: c26:null_A__U91 -> c38:c36 -> c48:c47:null_A__TAKE a__isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark U41 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c54 :: c8:null_A__U41 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK isNatIList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c56 :: c38:c36 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U51 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c57 :: c12:null_A__U51 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK isNatList :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c59 :: c41:c42:null_A__ISNATLIST -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U61 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c60 :: c16:null_A__U61 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U71 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c62 :: c20:null_A__U71 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U72 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c63 :: c22:null_A__U72 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK isNat :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c64 :: c33:c34:null_A__ISNAT -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK length :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c65 :: c45:null_A__LENGTH -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U91 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c67 :: c26:null_A__U91 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U92 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c68 :: c28:null_A__U92 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U93 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c69 :: c30:null_A__U93 -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK c70 :: c48:c47:null_A__TAKE -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK c71 :: c48:c47:null_A__TAKE -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK c72 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK c75 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK c8 :: c38:c36 -> c8:null_A__U41 c12 :: c41:c42:null_A__ISNATLIST -> c12:null_A__U51 c16 :: c38:c36 -> c16:null_A__U61 c33 :: c41:c42:null_A__ISNATLIST -> c33:c34:null_A__ISNAT c34 :: c33:c34:null_A__ISNAT -> c33:c34:null_A__ISNAT c36 :: c41:c42:null_A__ISNATLIST -> c38:c36 0 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c47 :: c38:c36 -> c48:c47:null_A__TAKE U11 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c51 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U21 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c52 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U31 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c53 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U42 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c55 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK U52 :: tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark c58 :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK -> 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tt:cons:take:s:U41:isNatIList:U51:isNatList:U61:U71:U72:isNat:length:U91:U92:U93:0:U11:U21:U31:U42:U52:U62:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__U51:null_a__U52:null_a__U61:null_a__U62:null_a__U71:null_a__U72:null_a__U81:null_a__U91:null_a__U92:null_a__U93:null_a__isNat:null_a__isNatIList:null_a__isNatList:null_a__length:null_a__take:null_mark null_A__U71 :: c20:null_A__U71 null_A__U72 :: c22:null_A__U72 null_A__U91 :: c26:null_A__U91 null_A__U92 :: c28:null_A__U92 null_A__U93 :: c30:null_A__U93 null_A__ISNATLIST :: c41:c42:null_A__ISNATLIST null_A__LENGTH :: c45:null_A__LENGTH null_A__TAKE :: c48:c47:null_A__TAKE null_MARK :: c54:c56:c57:c59:c60:c62:c63:c64:c65:c67:c68:c69:c70:c71:c72:c75:c51:c52:c53:c55:c58:c61:c66:null_MARK null_A__U41 :: c8:null_A__U41 null_A__U51 :: c12:null_A__U51 null_A__U61 :: c16:null_A__U61 null_A__ISNAT :: c33:c34:null_A__ISNAT const :: c38:c36 Rewrite Strategy: INNERMOST ---------------------------------------- (61) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 2 0 => 0 zeros => 3 nil => 1 null_a__zeros => 0 null_a__U11 => 0 null_a__U21 => 0 null_a__U31 => 0 null_a__U41 => 0 null_a__U42 => 0 null_a__U51 => 0 null_a__U52 => 0 null_a__U61 => 0 null_a__U62 => 0 null_a__U71 => 0 null_a__U72 => 0 null_a__U81 => 0 null_a__U91 => 0 null_a__U92 => 0 null_a__U93 => 0 null_a__isNat => 0 null_a__isNatIList => 0 null_a__isNatList => 0 null_a__length => 0 null_a__take => 0 null_mark => 0 null_A__U71 => 0 null_A__U72 => 0 null_A__U91 => 0 null_A__U92 => 0 null_A__U93 => 0 null_A__ISNATLIST => 0 null_A__LENGTH => 0 null_A__TAKE => 0 null_MARK => 0 null_A__U41 => 0 null_A__U51 => 0 null_A__U61 => 0 null_A__ISNAT => 0 const => 0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNAT(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__isNatList(z1), z1, z0) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__TAKE(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__isNatIList(z2), z2, z0, z1) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U41(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U41(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U51(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U61(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U71(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__isNat(z1), z0) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U72(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U72(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + A__U92(a__isNat(z1), z0, z1, z2) + A__ISNAT(z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U92(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 A__U92(z, z', z'', z4) -{ 1 }-> 1 + A__U93(a__isNat(z2), z0, z1, z2) + A__ISNAT(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 A__U93(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 A__U93(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U93(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U92(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U72(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 a__U11(z) -{ 0 }-> 2 :|: z = 2 a__U11(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U11(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z) -{ 0 }-> 2 :|: z = 2 a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z) -{ 0 }-> 2 :|: z = 2 a__U31(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U31(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z, z') -{ 0 }-> a__U42(a__isNatIList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U41(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U41(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U42(z) -{ 0 }-> 2 :|: z = 2 a__U42(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U42(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z') -{ 0 }-> a__U52(a__isNatList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U51(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U51(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U52(z) -{ 0 }-> 2 :|: z = 2 a__U52(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U52(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U61(z, z') -{ 0 }-> a__U62(a__isNatIList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U61(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U61(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U62(z) -{ 0 }-> 2 :|: z = 2 a__U62(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U62(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__isNat(z1), z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U71(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U71(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U72(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U72(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U72(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> a__U92(a__isNat(z1), z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> a__U93(a__isNat(z2), z0, z1, z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U92(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U92(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U93(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U93(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNat(z0)) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__isNatList(z0)) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__isNat(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__isNatList(z0)) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__isNat(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__isNat(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> a__U71(a__isNatList(z1), z1, z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__isNatIList(z2), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__isNatIList(z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__zeros :|: z = 3 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U93(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U92(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U72(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U71(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U52(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U51(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U42(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U41(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U31(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U71(tt, z0, z1) -> c20(A__U72(a__isNat(z1), z0), A__ISNAT(z1)) by A__U71(tt, x0, 0) -> c20(A__U72(tt, x0), A__ISNAT(0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, z0) -> c20(A__U72(isNat(z0), x0), A__ISNAT(z0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0), A__ISNAT(0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, z0) -> c20(A__U72(isNat(z0), x0), A__ISNAT(z0)) S tuples: A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0), A__ISNAT(0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, z0) -> c20(A__U72(isNat(z0), x0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U72_2, A__U91_4, A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3 Compound Symbols: c22_2, c26_2, c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) S tuples: A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U72_2, A__U91_4, A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3 Compound Symbols: c22_2, c26_2, c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, z0) -> c22(A__LENGTH(mark(z0)), MARK(z0)) by A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros), MARK(zeros)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, 0) -> c22(A__LENGTH(0), MARK(0)) A__U72(tt, tt) -> c22(A__LENGTH(tt), MARK(tt)) A__U72(tt, s(z0)) -> c22(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U72(tt, nil) -> c22(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros), MARK(zeros)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, 0) -> c22(A__LENGTH(0), MARK(0)) A__U72(tt, tt) -> c22(A__LENGTH(tt), MARK(tt)) A__U72(tt, s(z0)) -> c22(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U72(tt, nil) -> c22(A__LENGTH(nil), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros), MARK(zeros)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, 0) -> c22(A__LENGTH(0), MARK(0)) A__U72(tt, tt) -> c22(A__LENGTH(tt), MARK(tt)) A__U72(tt, s(z0)) -> c22(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U72(tt, nil) -> c22(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3, A__U72_2 Compound Symbols: c26_2, c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__U72(tt, 0) -> c22(A__LENGTH(0), MARK(0)) A__U72(tt, nil) -> c22(A__LENGTH(nil), MARK(nil)) A__U72(tt, tt) -> c22(A__LENGTH(tt), MARK(tt)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros), MARK(zeros)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, s(z0)) -> c22(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros), MARK(zeros)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, s(z0)) -> c22(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3, A__U72_2 Compound Symbols: c26_2, c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3, A__U72_2 Compound Symbols: c26_2, c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U91(tt, z0, z1, z2) -> c26(A__U92(a__isNat(z1), z0, z1, z2), A__ISNAT(z1)) by A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2), A__ISNAT(0)) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, z0, x2) -> c26(A__U92(isNat(z0), x0, z0, x2), A__ISNAT(z0)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2), A__ISNAT(0)) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, z0, x2) -> c26(A__U92(isNat(z0), x0, z0, x2), A__ISNAT(z0)) S tuples: A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2), A__ISNAT(0)) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, z0, x2) -> c26(A__U92(isNat(z0), x0, z0, x2), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3, A__U72_2, A__U91_4 Compound Symbols: c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) S tuples: A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U92_4, A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3, A__U72_2, A__U91_4 Compound Symbols: c28_2, c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U92(tt, z0, z1, z2) -> c28(A__U93(a__isNat(z2), z0, z1, z2), A__ISNAT(z2)) by A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0), A__ISNAT(0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, z0) -> c28(A__U93(isNat(z0), x0, x1, z0), A__ISNAT(z0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0), A__ISNAT(0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, z0) -> c28(A__U93(isNat(z0), x0, x1, z0), A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0), A__ISNAT(0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, z0) -> c28(A__U93(isNat(z0), x0, x1, z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4 Compound Symbols: c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__ISNATILIST_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4 Compound Symbols: c30_1, c38_2, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILIST(cons(z0, z1)) -> c38(A__U41(a__isNat(z0), z1), A__ISNAT(z0)) by A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1), A__ISNAT(0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c38(A__U41(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1), A__ISNAT(0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c38(A__U41(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1), A__ISNAT(0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c38(A__U41(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4 Compound Symbols: c30_1, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4 Compound Symbols: c30_1, c41_2, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATLIST(cons(z0, z1)) -> c41(A__U51(a__isNat(z0), z1), A__ISNAT(z0)) by A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1), A__ISNAT(0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c41(A__U51(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1), A__ISNAT(0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c41(A__U51(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1), A__ISNAT(0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c41(A__U51(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4 Compound Symbols: c30_1, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4 Compound Symbols: c30_1, c42_2, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATLIST(take(z0, z1)) -> c42(A__U61(a__isNat(z0), z1), A__ISNAT(z0)) by A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1), A__ISNAT(0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(z0, x1)) -> c42(A__U61(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1), A__ISNAT(0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(z0, x1)) -> c42(A__U61(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1), A__ISNAT(0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(z0, x1)) -> c42(A__U61(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1 Compound Symbols: c30_1, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1 Compound Symbols: c30_1, c45_2, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c45(A__U71(a__isNatList(z1), z1, z0), A__ISNATLIST(z1)) by A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0), A__ISNATLIST(nil)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c45(A__U71(isNatList(z0), z0, x0), A__ISNATLIST(z0)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0), A__ISNATLIST(nil)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c45(A__U71(isNatList(z0), z0, x0), A__ISNATLIST(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0), A__ISNATLIST(nil)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c45(A__U71(isNatList(z0), z0, x0), A__ISNATLIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, A__TAKE_2, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c48_2, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TAKE(s(z0), cons(z1, z2)) -> c48(A__U91(a__isNatIList(z2), z2, z0, z1), A__ISNATILIST(z2)) by A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(isNatIList(z0), z0, x0, x1), A__ISNATILIST(z0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(isNatIList(z0), z0, x0, x1), A__ISNATILIST(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(isNatIList(z0), z0, x0, x1), A__ISNATILIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c54_2, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1)) -> c54(A__U41(mark(z0), z1), MARK(z0)) by MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1), MARK(zeros)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(isNatIList(z0), x1)) -> c54(A__U41(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(isNatList(z0), x1)) -> c54(A__U41(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(isNat(z0), x1)) -> c54(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(cons(z0, z1), x1)) -> c54(A__U41(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U41(0, x1)) -> c54(A__U41(0, x1), MARK(0)) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c54(A__U41(s(mark(z0)), x1), MARK(s(z0))) MARK(U41(nil, x1)) -> c54(A__U41(nil, x1), MARK(nil)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1), MARK(zeros)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(isNatIList(z0), x1)) -> c54(A__U41(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(isNatList(z0), x1)) -> c54(A__U41(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(isNat(z0), x1)) -> c54(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(cons(z0, z1), x1)) -> c54(A__U41(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U41(0, x1)) -> c54(A__U41(0, x1), MARK(0)) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c54(A__U41(s(mark(z0)), x1), MARK(s(z0))) MARK(U41(nil, x1)) -> c54(A__U41(nil, x1), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1), MARK(zeros)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(isNatIList(z0), x1)) -> c54(A__U41(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(isNatList(z0), x1)) -> c54(A__U41(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(isNat(z0), x1)) -> c54(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(cons(z0, z1), x1)) -> c54(A__U41(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U41(0, x1)) -> c54(A__U41(0, x1), MARK(0)) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c54(A__U41(s(mark(z0)), x1), MARK(s(z0))) MARK(U41(nil, x1)) -> c54(A__U41(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U41(0, x1)) -> c54(A__U41(0, x1), MARK(0)) MARK(U41(nil, x1)) -> c54(A__U41(nil, x1), MARK(nil)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1), MARK(zeros)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(isNatIList(z0), x1)) -> c54(A__U41(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(isNatList(z0), x1)) -> c54(A__U41(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(isNat(z0), x1)) -> c54(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(cons(z0, z1), x1)) -> c54(A__U41(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c54(A__U41(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1), MARK(zeros)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(isNatIList(z0), x1)) -> c54(A__U41(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(isNatList(z0), x1)) -> c54(A__U41(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(isNat(z0), x1)) -> c54(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(cons(z0, z1), x1)) -> c54(A__U41(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c54(A__U41(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(isNatIList(z0), x1)) -> c54(A__U41(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(isNatList(z0), x1)) -> c54(A__U41(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(isNat(z0), x1)) -> c54(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(isNatIList(z0), x1)) -> c54(A__U41(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(isNatList(z0), x1)) -> c54(A__U41(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(isNat(z0), x1)) -> c54(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1 ---------------------------------------- (107) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c57_2, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U51(z0, z1)) -> c57(A__U51(mark(z0), z1), MARK(z0)) by MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1), MARK(zeros)) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(isNatIList(z0), x1)) -> c57(A__U51(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(isNatList(z0), x1)) -> c57(A__U51(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(isNat(z0), x1)) -> c57(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(cons(z0, z1), x1)) -> c57(A__U51(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U51(0, x1)) -> c57(A__U51(0, x1), MARK(0)) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c57(A__U51(s(mark(z0)), x1), MARK(s(z0))) MARK(U51(nil, x1)) -> c57(A__U51(nil, x1), MARK(nil)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1), MARK(zeros)) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(isNatIList(z0), x1)) -> c57(A__U51(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(isNatList(z0), x1)) -> c57(A__U51(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(isNat(z0), x1)) -> c57(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(cons(z0, z1), x1)) -> c57(A__U51(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U51(0, x1)) -> c57(A__U51(0, x1), MARK(0)) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c57(A__U51(s(mark(z0)), x1), MARK(s(z0))) MARK(U51(nil, x1)) -> c57(A__U51(nil, x1), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1), MARK(zeros)) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(isNatIList(z0), x1)) -> c57(A__U51(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(isNatList(z0), x1)) -> c57(A__U51(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(isNat(z0), x1)) -> c57(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(cons(z0, z1), x1)) -> c57(A__U51(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U51(0, x1)) -> c57(A__U51(0, x1), MARK(0)) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c57(A__U51(s(mark(z0)), x1), MARK(s(z0))) MARK(U51(nil, x1)) -> c57(A__U51(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U51(0, x1)) -> c57(A__U51(0, x1), MARK(0)) MARK(U51(nil, x1)) -> c57(A__U51(nil, x1), MARK(nil)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1), MARK(zeros)) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(isNatIList(z0), x1)) -> c57(A__U51(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(isNatList(z0), x1)) -> c57(A__U51(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(isNat(z0), x1)) -> c57(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(cons(z0, z1), x1)) -> c57(A__U51(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c57(A__U51(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1), MARK(zeros)) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(isNatIList(z0), x1)) -> c57(A__U51(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(isNatList(z0), x1)) -> c57(A__U51(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(isNat(z0), x1)) -> c57(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(cons(z0, z1), x1)) -> c57(A__U51(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1), MARK(tt)) MARK(U51(s(z0), x1)) -> c57(A__U51(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(isNatIList(z0), x1)) -> c57(A__U51(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(isNatList(z0), x1)) -> c57(A__U51(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(isNat(z0), x1)) -> c57(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(isNatIList(z0), x1)) -> c57(A__U51(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(isNatList(z0), x1)) -> c57(A__U51(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(isNat(z0), x1)) -> c57(A__U51(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1 ---------------------------------------- (115) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c60_2, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U61(z0, z1)) -> c60(A__U61(mark(z0), z1), MARK(z0)) by MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(isNatIList(z0), x1)) -> c60(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(isNatList(z0), x1)) -> c60(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(isNat(z0), x1)) -> c60(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(cons(z0, z1), x1)) -> c60(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(0, x1)) -> c60(A__U61(0, x1), MARK(0)) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c60(A__U61(s(mark(z0)), x1), MARK(s(z0))) MARK(U61(nil, x1)) -> c60(A__U61(nil, x1), MARK(nil)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(isNatIList(z0), x1)) -> c60(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(isNatList(z0), x1)) -> c60(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(isNat(z0), x1)) -> c60(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(cons(z0, z1), x1)) -> c60(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(0, x1)) -> c60(A__U61(0, x1), MARK(0)) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c60(A__U61(s(mark(z0)), x1), MARK(s(z0))) MARK(U61(nil, x1)) -> c60(A__U61(nil, x1), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(isNatIList(z0), x1)) -> c60(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(isNatList(z0), x1)) -> c60(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(isNat(z0), x1)) -> c60(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(cons(z0, z1), x1)) -> c60(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(0, x1)) -> c60(A__U61(0, x1), MARK(0)) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c60(A__U61(s(mark(z0)), x1), MARK(s(z0))) MARK(U61(nil, x1)) -> c60(A__U61(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U61(0, x1)) -> c60(A__U61(0, x1), MARK(0)) MARK(U61(nil, x1)) -> c60(A__U61(nil, x1), MARK(nil)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(isNatIList(z0), x1)) -> c60(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(isNatList(z0), x1)) -> c60(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(isNat(z0), x1)) -> c60(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(cons(z0, z1), x1)) -> c60(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c60(A__U61(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1), MARK(zeros)) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(isNatIList(z0), x1)) -> c60(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(isNatList(z0), x1)) -> c60(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(isNat(z0), x1)) -> c60(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(cons(z0, z1), x1)) -> c60(A__U61(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1), MARK(tt)) MARK(U61(s(z0), x1)) -> c60(A__U61(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(isNatIList(z0), x1)) -> c60(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(isNatList(z0), x1)) -> c60(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(isNat(z0), x1)) -> c60(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(isNatIList(z0), x1)) -> c60(A__U61(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(isNatList(z0), x1)) -> c60(A__U61(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(isNat(z0), x1)) -> c60(A__U61(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1 ---------------------------------------- (123) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c62_2, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U71(z0, z1, z2)) -> c62(A__U71(mark(z0), z1, z2), MARK(z0)) by MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2), MARK(zeros)) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(cons(z0, z1), x1, x2)) -> c62(A__U71(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U71(0, x1, x2)) -> c62(A__U71(0, x1, x2), MARK(0)) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c62(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U71(nil, x1, x2)) -> c62(A__U71(nil, x1, x2), MARK(nil)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2), MARK(zeros)) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(cons(z0, z1), x1, x2)) -> c62(A__U71(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U71(0, x1, x2)) -> c62(A__U71(0, x1, x2), MARK(0)) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c62(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U71(nil, x1, x2)) -> c62(A__U71(nil, x1, x2), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2), MARK(zeros)) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(cons(z0, z1), x1, x2)) -> c62(A__U71(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U71(0, x1, x2)) -> c62(A__U71(0, x1, x2), MARK(0)) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c62(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U71(nil, x1, x2)) -> c62(A__U71(nil, x1, x2), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U71(0, x1, x2)) -> c62(A__U71(0, x1, x2), MARK(0)) MARK(U71(nil, x1, x2)) -> c62(A__U71(nil, x1, x2), MARK(nil)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2), MARK(zeros)) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(cons(z0, z1), x1, x2)) -> c62(A__U71(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c62(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2), MARK(zeros)) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(cons(z0, z1), x1, x2)) -> c62(A__U71(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c62(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c63_2, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U72(z0, z1)) -> c63(A__U72(mark(z0), z1), MARK(z0)) by MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1), MARK(zeros)) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(cons(z0, z1), x1)) -> c63(A__U72(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U72(0, x1)) -> c63(A__U72(0, x1), MARK(0)) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1), MARK(tt)) MARK(U72(s(z0), x1)) -> c63(A__U72(s(mark(z0)), x1), MARK(s(z0))) MARK(U72(nil, x1)) -> c63(A__U72(nil, x1), MARK(nil)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1), MARK(zeros)) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(cons(z0, z1), x1)) -> c63(A__U72(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U72(0, x1)) -> c63(A__U72(0, x1), MARK(0)) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1), MARK(tt)) MARK(U72(s(z0), x1)) -> c63(A__U72(s(mark(z0)), x1), MARK(s(z0))) MARK(U72(nil, x1)) -> c63(A__U72(nil, x1), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1), MARK(zeros)) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(cons(z0, z1), x1)) -> c63(A__U72(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U72(0, x1)) -> c63(A__U72(0, x1), MARK(0)) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1), MARK(tt)) MARK(U72(s(z0), x1)) -> c63(A__U72(s(mark(z0)), x1), MARK(s(z0))) MARK(U72(nil, x1)) -> c63(A__U72(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U72(nil, x1)) -> c63(A__U72(nil, x1), MARK(nil)) MARK(U72(0, x1)) -> c63(A__U72(0, x1), MARK(0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1), MARK(zeros)) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(cons(z0, z1), x1)) -> c63(A__U72(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1), MARK(tt)) MARK(U72(s(z0), x1)) -> c63(A__U72(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1), MARK(zeros)) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(cons(z0, z1), x1)) -> c63(A__U72(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1), MARK(tt)) MARK(U72(s(z0), x1)) -> c63(A__U72(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c65_2, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c65(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c65(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c65(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c65(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c65(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c65(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c65(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c65(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c65(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c65(A__LENGTH(nil), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c65(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c65(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c65(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c65(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(nil)) -> c65(A__LENGTH(nil), MARK(nil)) MARK(length(0)) -> c65(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c65(A__LENGTH(tt), MARK(tt)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c65(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c65(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c67_2, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U91(z0, z1, z2, z3)) -> c67(A__U91(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(0, x1, x2, x3)) -> c67(A__U91(0, x1, x2, x3), MARK(0)) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c67(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U91(nil, x1, x2, x3)) -> c67(A__U91(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(0, x1, x2, x3)) -> c67(A__U91(0, x1, x2, x3), MARK(0)) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c67(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U91(nil, x1, x2, x3)) -> c67(A__U91(nil, x1, x2, x3), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(0, x1, x2, x3)) -> c67(A__U91(0, x1, x2, x3), MARK(0)) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c67(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U91(nil, x1, x2, x3)) -> c67(A__U91(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U91(nil, x1, x2, x3)) -> c67(A__U91(nil, x1, x2, x3), MARK(nil)) MARK(U91(0, x1, x2, x3)) -> c67(A__U91(0, x1, x2, x3), MARK(0)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c67(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c67(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c68_2, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U92(z0, z1, z2, z3)) -> c68(A__U92(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(A__U92(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U92(0, x1, x2, x3)) -> c68(A__U92(0, x1, x2, x3), MARK(0)) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3), MARK(tt)) MARK(U92(s(z0), x1, x2, x3)) -> c68(A__U92(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U92(nil, x1, x2, x3)) -> c68(A__U92(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(A__U92(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U92(0, x1, x2, x3)) -> c68(A__U92(0, x1, x2, x3), MARK(0)) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3), MARK(tt)) MARK(U92(s(z0), x1, x2, x3)) -> c68(A__U92(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U92(nil, x1, x2, x3)) -> c68(A__U92(nil, x1, x2, x3), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(A__U92(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U92(0, x1, x2, x3)) -> c68(A__U92(0, x1, x2, x3), MARK(0)) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3), MARK(tt)) MARK(U92(s(z0), x1, x2, x3)) -> c68(A__U92(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U92(nil, x1, x2, x3)) -> c68(A__U92(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2 ---------------------------------------- (151) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U92(0, x1, x2, x3)) -> c68(A__U92(0, x1, x2, x3), MARK(0)) MARK(U92(nil, x1, x2, x3)) -> c68(A__U92(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(A__U92(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3), MARK(tt)) MARK(U92(s(z0), x1, x2, x3)) -> c68(A__U92(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(A__U92(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3), MARK(tt)) MARK(U92(s(z0), x1, x2, x3)) -> c68(A__U92(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c69_2, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U93(z0, z1, z2, z3)) -> c69(A__U93(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(A__U93(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U93(0, x1, x2, x3)) -> c69(A__U93(0, x1, x2, x3), MARK(0)) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3), MARK(tt)) MARK(U93(s(z0), x1, x2, x3)) -> c69(A__U93(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U93(nil, x1, x2, x3)) -> c69(A__U93(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(A__U93(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U93(0, x1, x2, x3)) -> c69(A__U93(0, x1, x2, x3), MARK(0)) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3), MARK(tt)) MARK(U93(s(z0), x1, x2, x3)) -> c69(A__U93(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U93(nil, x1, x2, x3)) -> c69(A__U93(nil, x1, x2, x3), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> 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x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(A__U93(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U93(0, x1, x2, x3)) -> c69(A__U93(0, x1, x2, x3), MARK(0)) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3), MARK(tt)) MARK(U93(s(z0), x1, x2, x3)) -> c69(A__U93(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U93(nil, x1, x2, x3)) -> c69(A__U93(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U93(0, x1, x2, x3)) -> c69(A__U93(0, x1, x2, x3), MARK(0)) MARK(U93(nil, x1, x2, x3)) -> c69(A__U93(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(A__U93(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3), MARK(tt)) MARK(U93(s(z0), x1, x2, x3)) -> c69(A__U93(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(A__U93(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3), MARK(tt)) MARK(U93(s(z0), x1, x2, x3)) -> c69(A__U93(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c70_2, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c70(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c70(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c70(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c70(A__TAKE(nil, mark(x1)), MARK(nil)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), 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z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c70(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c70(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c70(A__TAKE(nil, mark(x1)), MARK(nil)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c70(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c70(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c70(A__TAKE(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2 ---------------------------------------- (163) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(nil, x1)) -> c70(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(tt, x1)) -> c70(A__TAKE(tt, mark(x1)), MARK(tt)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), 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MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c70(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c70(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> 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x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c71_2, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c71(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c71(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c71(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c71(A__TAKE(nil, mark(x1)), MARK(x1)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, 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c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c71(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c71(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c71(A__TAKE(nil, mark(x1)), MARK(x1)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, 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MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), 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MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c71(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c71(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c71(A__TAKE(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, 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MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> 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MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(a__isNatList(z0)), x0), A__ISNAT(length(z0))) by A__U71(tt, x0, length(x1)) -> c20(A__U72(U11(a__isNatList(x1)), x0), A__ISNAT(length(x1))) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), 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z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(x1)) -> c20(A__U72(U11(a__isNatList(x1)), x0), A__ISNAT(length(x1))) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(x1)) -> c20(A__U72(U11(a__isNatList(x1)), x0), A__ISNAT(length(x1))) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> 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x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), 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x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), 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z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_2, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(a__isNat(z0)), x0), A__ISNAT(s(z0))) by A__U71(tt, x0, s(x1)) -> c20(A__U72(U21(a__isNat(x1)), x0), A__ISNAT(s(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), 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MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), 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MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, 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x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(x1)) -> c20(A__U72(U21(a__isNat(x1)), x0), A__ISNAT(s(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(x1)) -> c20(A__U72(U21(a__isNat(x1)), x0), A__ISNAT(s(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U11(z0)) -> c22(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) by A__U72(tt, U11(x0)) -> c22(A__LENGTH(U11(mark(x0))), MARK(U11(x0))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> 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MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), 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MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), 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MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), 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c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(x0)) -> c22(A__LENGTH(U11(mark(x0))), MARK(U11(x0))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), 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MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(x0)) -> c22(A__LENGTH(U11(mark(x0))), MARK(U11(x0))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U21(z0)) -> c22(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) by A__U72(tt, U21(x0)) -> c22(A__LENGTH(U21(mark(x0))), MARK(U21(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(x0)) -> c22(A__LENGTH(U21(mark(x0))), MARK(U21(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) 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MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, 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MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(x0)) -> c22(A__LENGTH(U21(mark(x0))), MARK(U21(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), 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c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> 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c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U31(z0)) -> c22(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) by A__U72(tt, U31(x0)) -> c22(A__LENGTH(U31(mark(x0))), MARK(U31(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, 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c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) 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MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), 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MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(x0)) -> c22(A__LENGTH(U31(mark(x0))), MARK(U31(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), 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MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> 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c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) 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MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), 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MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(x0)) -> c22(A__LENGTH(U31(mark(x0))), MARK(U31(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> 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c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, 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c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> 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c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U41(z0, z1)) -> c22(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) by A__U72(tt, U41(x0, z1)) -> c22(A__LENGTH(U41(mark(x0), z1)), MARK(U41(x0, z1))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1)), MARK(U41(0, x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1)), MARK(U41(nil, x1))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> 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-> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(x0, z1)) -> c22(A__LENGTH(U41(mark(x0), z1)), MARK(U41(x0, z1))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1)), MARK(U41(0, x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1)), MARK(U41(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), 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x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(x0, z1)) -> c22(A__LENGTH(U41(mark(x0), z1)), MARK(U41(x0, z1))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1)), MARK(U41(0, x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1)), MARK(U41(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) 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MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), 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c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), 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c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U42(z0)) -> c22(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) by A__U72(tt, U42(x0)) -> c22(A__LENGTH(U42(mark(x0))), MARK(U42(x0))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, 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A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(x0)) -> c22(A__LENGTH(U42(mark(x0))), MARK(U42(x0))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, 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c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, 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c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(x0)) -> c22(A__LENGTH(U42(mark(x0))), MARK(U42(x0))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> 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c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), 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MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, 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U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> 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z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), 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MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> 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c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) by A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(zeros)) -> c22(A__LENGTH(tt), MARK(isNatIList(zeros))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(isNatIList(z0)), MARK(isNatIList(z0))) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, 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MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) 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c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(zeros)) -> c22(A__LENGTH(tt), MARK(isNatIList(zeros))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(isNatIList(z0)), MARK(isNatIList(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), 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c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(zeros)) -> c22(A__LENGTH(tt), MARK(isNatIList(zeros))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(isNatIList(z0)), MARK(isNatIList(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), 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MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), 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MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, 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x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) 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x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> 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MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), 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A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) 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A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U51(z0, z1)) -> c22(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) by A__U72(tt, U51(x0, z1)) -> c22(A__LENGTH(U51(mark(x0), z1)), MARK(U51(x0, z1))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1)), MARK(U51(0, x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1)), MARK(U51(nil, x1))) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), 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z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(x0, z1)) -> c22(A__LENGTH(U51(mark(x0), z1)), MARK(U51(x0, z1))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1)), MARK(U51(0, x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1)), MARK(U51(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> 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c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(x0, z1)) -> c22(A__LENGTH(U51(mark(x0), z1)), MARK(U51(x0, z1))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1)), MARK(U51(0, x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1)), MARK(U51(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> 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MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, 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A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) 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A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), 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A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U52(z0)) -> c22(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) by A__U72(tt, U52(x0)) -> c22(A__LENGTH(U52(mark(x0))), MARK(U52(x0))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> 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MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) 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U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(x0)) -> c22(A__LENGTH(U52(mark(x0))), MARK(U52(x0))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, 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MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> 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A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(x0)) -> c22(A__LENGTH(U52(mark(x0))), MARK(U52(x0))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) 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MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, 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-> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> 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A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, 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-> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), 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c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (211) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) by A__U72(tt, isNatList(nil)) -> c22(A__LENGTH(tt), MARK(isNatList(nil))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(isNatList(z0)), MARK(isNatList(z0))) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> 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c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(nil)) -> c22(A__LENGTH(tt), MARK(isNatList(nil))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(isNatList(z0)), MARK(isNatList(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) 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MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), 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U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> 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c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(nil)) -> c22(A__LENGTH(tt), MARK(isNatList(nil))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(z0)) -> c22(A__LENGTH(isNatList(z0)), MARK(isNatList(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), 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c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) 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MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), 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U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> 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c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U61(z0, z1)) -> c22(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) by A__U72(tt, U61(x0, z1)) -> c22(A__LENGTH(U61(mark(x0), z1)), MARK(U61(x0, z1))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1)), MARK(U61(0, x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1)), MARK(U61(nil, x1))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), 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MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, 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A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(x0, z1)) -> c22(A__LENGTH(U61(mark(x0), z1)), MARK(U61(x0, z1))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1)), MARK(U61(0, x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1)), MARK(U61(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), 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c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(x0, z1)) -> c22(A__LENGTH(U61(mark(x0), z1)), MARK(U61(x0, z1))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1)), MARK(U61(0, x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1)), MARK(U61(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), 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x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), 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MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, 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c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), 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c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U62(z0)) -> c22(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) by A__U72(tt, U62(x0)) -> c22(A__LENGTH(U62(mark(x0))), MARK(U62(x0))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> 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MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> 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c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> 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MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), 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c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), 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A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, 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c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, 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c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, 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A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> 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z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(x0)) -> c22(A__LENGTH(U62(mark(x0))), MARK(U62(x0))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), 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MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), 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MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> 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A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), 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A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), 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A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, 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c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (223) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U71(z0, z1, z2)) -> c22(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) by A__U72(tt, U71(x0, z1, z2)) -> c22(A__LENGTH(U71(mark(x0), z1, z2)), MARK(U71(x0, z1, z2))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2)), MARK(U71(0, x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2)), MARK(U71(nil, x1, x2))) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, 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A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(x0, z1, z2)) -> c22(A__LENGTH(U71(mark(x0), z1, z2)), MARK(U71(x0, z1, z2))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2)), MARK(U71(0, x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2)), MARK(U71(nil, x1, x2))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), 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A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(x0, z1, z2)) -> c22(A__LENGTH(U71(mark(x0), z1, z2)), MARK(U71(x0, z1, z2))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2)), MARK(U71(0, x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2)), MARK(U71(nil, x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), 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c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, 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-> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> 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c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) 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U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> 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c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (227) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U72(z0, z1)) -> c22(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) by A__U72(tt, U72(x0, z1)) -> c22(A__LENGTH(U72(mark(x0), z1)), MARK(U72(x0, z1))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1)), MARK(U72(0, x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1)), MARK(U72(nil, x1))) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), 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c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> 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A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), 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A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(x0, z1)) -> c22(A__LENGTH(U72(mark(x0), z1)), MARK(U72(x0, z1))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1)), MARK(U72(0, x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1)), MARK(U72(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> 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MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(x0, z1)) -> c22(A__LENGTH(U72(mark(x0), z1)), MARK(U72(x0, z1))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1)), MARK(U72(0, x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1)), MARK(U72(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> 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MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), 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MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), 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c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), 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A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> 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MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, isNat(z0)) -> c22(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) by A__U72(tt, isNat(0)) -> c22(A__LENGTH(tt), MARK(isNat(0))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(isNat(z0)), MARK(isNat(z0))) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> 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-> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), 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MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(0)) -> c22(A__LENGTH(tt), MARK(isNat(0))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(isNat(z0)), MARK(isNat(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, 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MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), 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U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> 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c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(0)) -> c22(A__LENGTH(tt), MARK(isNat(0))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(z0)) -> c22(A__LENGTH(isNat(z0)), MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> 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-> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, 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-> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) 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c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), 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c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (235) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, length(z0)) -> c22(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by A__U72(tt, length(x0)) -> c22(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0)), MARK(length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil)), MARK(length(nil))) ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), 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MARK(x1)) MARK(take(s(z0), x1)) -> c71(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c71(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c71(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c71(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c71(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c71(MARK(x1)) MARK(take(tt, x1)) -> c71(MARK(x1)) MARK(take(nil, x1)) -> c71(MARK(x1)) A__U71(tt, x0, length(nil)) -> c20(A__U72(a__U11(tt), x0), A__ISNAT(length(nil))) A__U71(tt, x0, length(cons(z0, z1))) -> c20(A__U72(a__U11(a__U51(a__isNat(z0), z1)), x0), A__ISNAT(length(cons(z0, z1)))) A__U71(tt, x0, length(take(z0, z1))) -> c20(A__U72(a__U11(a__U61(a__isNat(z0), z1)), x0), A__ISNAT(length(take(z0, z1)))) A__U71(tt, x0, length(z0)) -> c20(A__U72(a__U11(isNatList(z0)), x0), A__ISNAT(length(z0))) A__U71(tt, x0, length(x1)) -> c20(A__ISNAT(length(x1))) A__U71(tt, x0, s(0)) -> c20(A__U72(a__U21(tt), x0), A__ISNAT(s(0))) A__U71(tt, x0, s(length(z0))) -> c20(A__U72(a__U21(a__U11(a__isNatList(z0))), x0), A__ISNAT(s(length(z0)))) A__U71(tt, x0, s(s(z0))) -> c20(A__U72(a__U21(a__U21(a__isNat(z0))), x0), A__ISNAT(s(s(z0)))) A__U71(tt, x0, s(z0)) -> c20(A__U72(a__U21(isNat(z0)), x0), A__ISNAT(s(z0))) A__U71(tt, x0, s(x1)) -> c20(A__ISNAT(s(x1))) A__U72(tt, U11(zeros)) -> c22(A__LENGTH(a__U11(a__zeros)), MARK(U11(zeros))) A__U72(tt, U11(U11(z0))) -> c22(A__LENGTH(a__U11(a__U11(mark(z0)))), MARK(U11(U11(z0)))) A__U72(tt, U11(U21(z0))) -> c22(A__LENGTH(a__U11(a__U21(mark(z0)))), MARK(U11(U21(z0)))) A__U72(tt, U11(U31(z0))) -> c22(A__LENGTH(a__U11(a__U31(mark(z0)))), MARK(U11(U31(z0)))) A__U72(tt, U11(U41(z0, z1))) -> c22(A__LENGTH(a__U11(a__U41(mark(z0), z1))), MARK(U11(U41(z0, z1)))) A__U72(tt, U11(U42(z0))) -> c22(A__LENGTH(a__U11(a__U42(mark(z0)))), MARK(U11(U42(z0)))) A__U72(tt, U11(isNatIList(z0))) -> c22(A__LENGTH(a__U11(a__isNatIList(z0))), MARK(U11(isNatIList(z0)))) A__U72(tt, U11(U51(z0, z1))) -> c22(A__LENGTH(a__U11(a__U51(mark(z0), z1))), MARK(U11(U51(z0, z1)))) A__U72(tt, U11(U52(z0))) -> c22(A__LENGTH(a__U11(a__U52(mark(z0)))), MARK(U11(U52(z0)))) A__U72(tt, U11(isNatList(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(U11(isNatList(z0)))) A__U72(tt, U11(U61(z0, z1))) -> c22(A__LENGTH(a__U11(a__U61(mark(z0), z1))), MARK(U11(U61(z0, z1)))) A__U72(tt, U11(U62(z0))) -> c22(A__LENGTH(a__U11(a__U62(mark(z0)))), MARK(U11(U62(z0)))) A__U72(tt, U11(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U11(a__U71(mark(z0), z1, z2))), MARK(U11(U71(z0, z1, z2)))) A__U72(tt, U11(U72(z0, z1))) -> c22(A__LENGTH(a__U11(a__U72(mark(z0), z1))), MARK(U11(U72(z0, z1)))) A__U72(tt, U11(isNat(z0))) -> c22(A__LENGTH(a__U11(a__isNat(z0))), MARK(U11(isNat(z0)))) A__U72(tt, U11(length(z0))) -> c22(A__LENGTH(a__U11(a__length(mark(z0)))), MARK(U11(length(z0)))) A__U72(tt, U11(U81(z0))) -> c22(A__LENGTH(a__U11(a__U81(mark(z0)))), MARK(U11(U81(z0)))) A__U72(tt, U11(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3))), MARK(U11(U91(z0, z1, z2, z3)))) A__U72(tt, U11(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U92(mark(z0), z1, z2, z3))), MARK(U11(U92(z0, z1, z2, z3)))) A__U72(tt, U11(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U11(a__U93(mark(z0), z1, z2, z3))), MARK(U11(U93(z0, z1, z2, z3)))) A__U72(tt, U11(take(z0, z1))) -> c22(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)))), MARK(U11(take(z0, z1)))) A__U72(tt, U11(cons(z0, z1))) -> c22(A__LENGTH(a__U11(cons(mark(z0), z1))), MARK(U11(cons(z0, z1)))) A__U72(tt, U11(0)) -> c22(A__LENGTH(a__U11(0)), MARK(U11(0))) A__U72(tt, U11(tt)) -> c22(A__LENGTH(a__U11(tt)), MARK(U11(tt))) A__U72(tt, U11(s(z0))) -> c22(A__LENGTH(a__U11(s(mark(z0)))), MARK(U11(s(z0)))) A__U72(tt, U11(nil)) -> c22(A__LENGTH(a__U11(nil)), MARK(U11(nil))) A__U72(tt, U11(x0)) -> c22(MARK(U11(x0))) A__U72(tt, U21(zeros)) -> c22(A__LENGTH(a__U21(a__zeros)), MARK(U21(zeros))) A__U72(tt, U21(U11(z0))) -> c22(A__LENGTH(a__U21(a__U11(mark(z0)))), MARK(U21(U11(z0)))) A__U72(tt, U21(U21(z0))) -> c22(A__LENGTH(a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0)))) A__U72(tt, U21(U31(z0))) -> c22(A__LENGTH(a__U21(a__U31(mark(z0)))), MARK(U21(U31(z0)))) A__U72(tt, U21(U41(z0, z1))) -> c22(A__LENGTH(a__U21(a__U41(mark(z0), z1))), MARK(U21(U41(z0, z1)))) A__U72(tt, U21(U42(z0))) -> c22(A__LENGTH(a__U21(a__U42(mark(z0)))), MARK(U21(U42(z0)))) A__U72(tt, U21(isNatIList(z0))) -> c22(A__LENGTH(a__U21(a__isNatIList(z0))), MARK(U21(isNatIList(z0)))) A__U72(tt, U21(U51(z0, z1))) -> c22(A__LENGTH(a__U21(a__U51(mark(z0), z1))), MARK(U21(U51(z0, z1)))) A__U72(tt, U21(U52(z0))) -> c22(A__LENGTH(a__U21(a__U52(mark(z0)))), MARK(U21(U52(z0)))) A__U72(tt, U21(isNatList(z0))) -> c22(A__LENGTH(a__U21(a__isNatList(z0))), MARK(U21(isNatList(z0)))) A__U72(tt, U21(U61(z0, z1))) -> c22(A__LENGTH(a__U21(a__U61(mark(z0), z1))), MARK(U21(U61(z0, z1)))) A__U72(tt, U21(U62(z0))) -> c22(A__LENGTH(a__U21(a__U62(mark(z0)))), MARK(U21(U62(z0)))) A__U72(tt, U21(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U21(a__U71(mark(z0), z1, z2))), MARK(U21(U71(z0, z1, z2)))) A__U72(tt, U21(U72(z0, z1))) -> c22(A__LENGTH(a__U21(a__U72(mark(z0), z1))), MARK(U21(U72(z0, z1)))) A__U72(tt, U21(isNat(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(U21(isNat(z0)))) A__U72(tt, U21(length(z0))) -> c22(A__LENGTH(a__U21(a__length(mark(z0)))), MARK(U21(length(z0)))) A__U72(tt, U21(U81(z0))) -> c22(A__LENGTH(a__U21(a__U81(mark(z0)))), MARK(U21(U81(z0)))) A__U72(tt, U21(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3))), MARK(U21(U91(z0, z1, z2, z3)))) A__U72(tt, U21(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U92(mark(z0), z1, z2, z3))), MARK(U21(U92(z0, z1, z2, z3)))) A__U72(tt, U21(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U21(a__U93(mark(z0), z1, z2, z3))), MARK(U21(U93(z0, z1, z2, z3)))) A__U72(tt, U21(take(z0, z1))) -> c22(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)))), MARK(U21(take(z0, z1)))) A__U72(tt, U21(cons(z0, z1))) -> c22(A__LENGTH(a__U21(cons(mark(z0), z1))), MARK(U21(cons(z0, z1)))) A__U72(tt, U21(0)) -> c22(A__LENGTH(a__U21(0)), MARK(U21(0))) A__U72(tt, U21(tt)) -> c22(A__LENGTH(a__U21(tt)), MARK(U21(tt))) A__U72(tt, U21(s(z0))) -> c22(A__LENGTH(a__U21(s(mark(z0)))), MARK(U21(s(z0)))) A__U72(tt, U21(nil)) -> c22(A__LENGTH(a__U21(nil)), MARK(U21(nil))) A__U72(tt, U21(x0)) -> c22(MARK(U21(x0))) A__U72(tt, U31(zeros)) -> c22(A__LENGTH(a__U31(a__zeros)), MARK(U31(zeros))) A__U72(tt, U31(U11(z0))) -> c22(A__LENGTH(a__U31(a__U11(mark(z0)))), MARK(U31(U11(z0)))) A__U72(tt, U31(U21(z0))) -> c22(A__LENGTH(a__U31(a__U21(mark(z0)))), MARK(U31(U21(z0)))) A__U72(tt, U31(U31(z0))) -> c22(A__LENGTH(a__U31(a__U31(mark(z0)))), MARK(U31(U31(z0)))) A__U72(tt, U31(U41(z0, z1))) -> c22(A__LENGTH(a__U31(a__U41(mark(z0), z1))), MARK(U31(U41(z0, z1)))) A__U72(tt, U31(U42(z0))) -> c22(A__LENGTH(a__U31(a__U42(mark(z0)))), MARK(U31(U42(z0)))) A__U72(tt, U31(isNatIList(z0))) -> c22(A__LENGTH(a__U31(a__isNatIList(z0))), MARK(U31(isNatIList(z0)))) A__U72(tt, U31(U51(z0, z1))) -> c22(A__LENGTH(a__U31(a__U51(mark(z0), z1))), MARK(U31(U51(z0, z1)))) A__U72(tt, U31(U52(z0))) -> c22(A__LENGTH(a__U31(a__U52(mark(z0)))), MARK(U31(U52(z0)))) A__U72(tt, U31(isNatList(z0))) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(U31(isNatList(z0)))) A__U72(tt, U31(U61(z0, z1))) -> c22(A__LENGTH(a__U31(a__U61(mark(z0), z1))), MARK(U31(U61(z0, z1)))) A__U72(tt, U31(U62(z0))) -> c22(A__LENGTH(a__U31(a__U62(mark(z0)))), MARK(U31(U62(z0)))) A__U72(tt, U31(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U31(a__U71(mark(z0), z1, z2))), MARK(U31(U71(z0, z1, z2)))) A__U72(tt, U31(U72(z0, z1))) -> c22(A__LENGTH(a__U31(a__U72(mark(z0), z1))), MARK(U31(U72(z0, z1)))) A__U72(tt, U31(isNat(z0))) -> c22(A__LENGTH(a__U31(a__isNat(z0))), MARK(U31(isNat(z0)))) A__U72(tt, U31(length(z0))) -> c22(A__LENGTH(a__U31(a__length(mark(z0)))), MARK(U31(length(z0)))) A__U72(tt, U31(U81(z0))) -> c22(A__LENGTH(a__U31(a__U81(mark(z0)))), MARK(U31(U81(z0)))) A__U72(tt, U31(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U91(mark(z0), z1, z2, z3))), MARK(U31(U91(z0, z1, z2, z3)))) A__U72(tt, U31(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U92(mark(z0), z1, z2, z3))), MARK(U31(U92(z0, z1, z2, z3)))) A__U72(tt, U31(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U31(a__U93(mark(z0), z1, z2, z3))), MARK(U31(U93(z0, z1, z2, z3)))) A__U72(tt, U31(take(z0, z1))) -> c22(A__LENGTH(a__U31(a__take(mark(z0), mark(z1)))), MARK(U31(take(z0, z1)))) A__U72(tt, U31(cons(z0, z1))) -> c22(A__LENGTH(a__U31(cons(mark(z0), z1))), MARK(U31(cons(z0, z1)))) A__U72(tt, U31(0)) -> c22(A__LENGTH(a__U31(0)), MARK(U31(0))) A__U72(tt, U31(tt)) -> c22(A__LENGTH(a__U31(tt)), MARK(U31(tt))) A__U72(tt, U31(s(z0))) -> c22(A__LENGTH(a__U31(s(mark(z0)))), MARK(U31(s(z0)))) A__U72(tt, U31(nil)) -> c22(A__LENGTH(a__U31(nil)), MARK(U31(nil))) A__U72(tt, U31(x0)) -> c22(MARK(U31(x0))) A__U72(tt, U41(zeros, x1)) -> c22(A__LENGTH(a__U41(a__zeros, x1)), MARK(U41(zeros, x1))) A__U72(tt, U41(U11(z0), x1)) -> c22(A__LENGTH(a__U41(a__U11(mark(z0)), x1)), MARK(U41(U11(z0), x1))) A__U72(tt, U41(U21(z0), x1)) -> c22(A__LENGTH(a__U41(a__U21(mark(z0)), x1)), MARK(U41(U21(z0), x1))) A__U72(tt, U41(U31(z0), x1)) -> c22(A__LENGTH(a__U41(a__U31(mark(z0)), x1)), MARK(U41(U31(z0), x1))) A__U72(tt, U41(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U41(mark(z0), z1), x1)), MARK(U41(U41(z0, z1), x1))) A__U72(tt, U41(U42(z0), x1)) -> c22(A__LENGTH(a__U41(a__U42(mark(z0)), x1)), MARK(U41(U42(z0), x1))) A__U72(tt, U41(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatIList(z0), x1)), MARK(U41(isNatIList(z0), x1))) A__U72(tt, U41(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U51(mark(z0), z1), x1)), MARK(U41(U51(z0, z1), x1))) A__U72(tt, U41(U52(z0), x1)) -> c22(A__LENGTH(a__U41(a__U52(mark(z0)), x1)), MARK(U41(U52(z0), x1))) A__U72(tt, U41(isNatList(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNatList(z0), x1)), MARK(U41(isNatList(z0), x1))) A__U72(tt, U41(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U61(mark(z0), z1), x1)), MARK(U41(U61(z0, z1), x1))) A__U72(tt, U41(U62(z0), x1)) -> c22(A__LENGTH(a__U41(a__U62(mark(z0)), x1)), MARK(U41(U62(z0), x1))) A__U72(tt, U41(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(U41(U71(z0, z1, z2), x1))) A__U72(tt, U41(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__U72(mark(z0), z1), x1)), MARK(U41(U72(z0, z1), x1))) A__U72(tt, U41(isNat(z0), x1)) -> c22(A__LENGTH(a__U41(a__isNat(z0), x1)), MARK(U41(isNat(z0), x1))) A__U72(tt, U41(length(z0), x1)) -> c22(A__LENGTH(a__U41(a__length(mark(z0)), x1)), MARK(U41(length(z0), x1))) A__U72(tt, U41(U81(z0), x1)) -> c22(A__LENGTH(a__U41(a__U81(mark(z0)), x1)), MARK(U41(U81(z0), x1))) A__U72(tt, U41(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U41(U91(z0, z1, z2, z3), x1))) A__U72(tt, U41(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U41(U92(z0, z1, z2, z3), x1))) A__U72(tt, U41(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U41(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U41(U93(z0, z1, z2, z3), x1))) A__U72(tt, U41(take(z0, z1), x1)) -> c22(A__LENGTH(a__U41(a__take(mark(z0), mark(z1)), x1)), MARK(U41(take(z0, z1), x1))) A__U72(tt, U41(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U41(cons(mark(z0), z1), x1)), MARK(U41(cons(z0, z1), x1))) A__U72(tt, U41(tt, x1)) -> c22(A__LENGTH(a__U41(tt, x1)), MARK(U41(tt, x1))) A__U72(tt, U41(s(z0), x1)) -> c22(A__LENGTH(a__U41(s(mark(z0)), x1)), MARK(U41(s(z0), x1))) A__U72(tt, U41(x0, z1)) -> c22(MARK(U41(x0, z1))) A__U72(tt, U41(0, x1)) -> c22(A__LENGTH(a__U41(0, x1))) A__U72(tt, U41(nil, x1)) -> c22(A__LENGTH(a__U41(nil, x1))) A__U72(tt, U42(zeros)) -> c22(A__LENGTH(a__U42(a__zeros)), MARK(U42(zeros))) A__U72(tt, U42(U11(z0))) -> c22(A__LENGTH(a__U42(a__U11(mark(z0)))), MARK(U42(U11(z0)))) A__U72(tt, U42(U21(z0))) -> c22(A__LENGTH(a__U42(a__U21(mark(z0)))), MARK(U42(U21(z0)))) A__U72(tt, U42(U31(z0))) -> c22(A__LENGTH(a__U42(a__U31(mark(z0)))), MARK(U42(U31(z0)))) A__U72(tt, U42(U41(z0, z1))) -> c22(A__LENGTH(a__U42(a__U41(mark(z0), z1))), MARK(U42(U41(z0, z1)))) A__U72(tt, U42(U42(z0))) -> c22(A__LENGTH(a__U42(a__U42(mark(z0)))), MARK(U42(U42(z0)))) A__U72(tt, U42(isNatIList(z0))) -> c22(A__LENGTH(a__U42(a__isNatIList(z0))), MARK(U42(isNatIList(z0)))) A__U72(tt, U42(U51(z0, z1))) -> c22(A__LENGTH(a__U42(a__U51(mark(z0), z1))), MARK(U42(U51(z0, z1)))) A__U72(tt, U42(U52(z0))) -> c22(A__LENGTH(a__U42(a__U52(mark(z0)))), MARK(U42(U52(z0)))) A__U72(tt, U42(isNatList(z0))) -> c22(A__LENGTH(a__U42(a__isNatList(z0))), MARK(U42(isNatList(z0)))) A__U72(tt, U42(U61(z0, z1))) -> c22(A__LENGTH(a__U42(a__U61(mark(z0), z1))), MARK(U42(U61(z0, z1)))) A__U72(tt, U42(U62(z0))) -> c22(A__LENGTH(a__U42(a__U62(mark(z0)))), MARK(U42(U62(z0)))) A__U72(tt, U42(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U42(a__U71(mark(z0), z1, z2))), MARK(U42(U71(z0, z1, z2)))) A__U72(tt, U42(U72(z0, z1))) -> c22(A__LENGTH(a__U42(a__U72(mark(z0), z1))), MARK(U42(U72(z0, z1)))) A__U72(tt, U42(isNat(z0))) -> c22(A__LENGTH(a__U42(a__isNat(z0))), MARK(U42(isNat(z0)))) A__U72(tt, U42(length(z0))) -> c22(A__LENGTH(a__U42(a__length(mark(z0)))), MARK(U42(length(z0)))) A__U72(tt, U42(U81(z0))) -> c22(A__LENGTH(a__U42(a__U81(mark(z0)))), MARK(U42(U81(z0)))) A__U72(tt, U42(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U91(mark(z0), z1, z2, z3))), MARK(U42(U91(z0, z1, z2, z3)))) A__U72(tt, U42(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U92(mark(z0), z1, z2, z3))), MARK(U42(U92(z0, z1, z2, z3)))) A__U72(tt, U42(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U42(a__U93(mark(z0), z1, z2, z3))), MARK(U42(U93(z0, z1, z2, z3)))) A__U72(tt, U42(take(z0, z1))) -> c22(A__LENGTH(a__U42(a__take(mark(z0), mark(z1)))), MARK(U42(take(z0, z1)))) A__U72(tt, U42(cons(z0, z1))) -> c22(A__LENGTH(a__U42(cons(mark(z0), z1))), MARK(U42(cons(z0, z1)))) A__U72(tt, U42(0)) -> c22(A__LENGTH(a__U42(0)), MARK(U42(0))) A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(x0)) -> c22(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0)), MARK(length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil)), MARK(length(nil))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> 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MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> 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c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(x0)) -> c22(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0)), MARK(length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil)), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (237) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), 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MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, 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MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), 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MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1))) -> c71(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(take(x0, U52(z0))) -> c71(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(U52(z0))) MARK(take(x0, isNatList(z0))) -> c71(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U61(z0, z1))) -> c71(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(take(x0, U62(z0))) -> c71(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(U62(z0))) MARK(take(x0, U71(z0, z1, z2))) -> c71(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(take(x0, U72(z0, z1))) -> c71(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(take(x0, isNat(z0))) -> c71(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, length(z0))) -> c71(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c71(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, U92(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(take(x0, U93(z0, z1, z2, z3))) -> c71(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c71(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c71(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c71(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c71(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0), x1)) -> c71(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0), x1)) -> c71(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U31(z0), x1)) -> c71(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1), x1)) -> c71(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U42(z0), x1)) -> c71(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c71(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1), x1)) -> c71(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U52(z0), x1)) -> c71(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c71(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1), x1)) -> c71(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U62(z0), x1)) -> c71(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1, z2), x1)) -> c71(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U72(z0, z1), x1)) -> c71(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c71(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c71(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c71(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U92(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U93(z0, z1, z2, z3), x1)) -> c71(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c71(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c71(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> 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A__U72(tt, U42(tt)) -> c22(A__LENGTH(a__U42(tt)), MARK(U42(tt))) A__U72(tt, U42(s(z0))) -> c22(A__LENGTH(a__U42(s(mark(z0)))), MARK(U42(s(z0)))) A__U72(tt, U42(nil)) -> c22(A__LENGTH(a__U42(nil)), MARK(U42(nil))) A__U72(tt, U42(x0)) -> c22(MARK(U42(x0))) A__U72(tt, isNatIList(z0)) -> c22(A__LENGTH(a__U31(a__isNatList(z0))), MARK(isNatIList(z0))) A__U72(tt, isNatIList(cons(z0, z1))) -> c22(A__LENGTH(a__U41(a__isNat(z0), z1)), MARK(isNatIList(cons(z0, z1)))) A__U72(tt, isNatIList(zeros)) -> c22(MARK(isNatIList(zeros))) A__U72(tt, isNatIList(z0)) -> c22(MARK(isNatIList(z0))) A__U72(tt, U51(zeros, x1)) -> c22(A__LENGTH(a__U51(a__zeros, x1)), MARK(U51(zeros, x1))) A__U72(tt, U51(U11(z0), x1)) -> c22(A__LENGTH(a__U51(a__U11(mark(z0)), x1)), MARK(U51(U11(z0), x1))) A__U72(tt, U51(U21(z0), x1)) -> c22(A__LENGTH(a__U51(a__U21(mark(z0)), x1)), MARK(U51(U21(z0), x1))) A__U72(tt, U51(U31(z0), x1)) -> c22(A__LENGTH(a__U51(a__U31(mark(z0)), x1)), MARK(U51(U31(z0), x1))) A__U72(tt, U51(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U41(mark(z0), z1), x1)), MARK(U51(U41(z0, z1), x1))) A__U72(tt, U51(U42(z0), x1)) -> c22(A__LENGTH(a__U51(a__U42(mark(z0)), x1)), MARK(U51(U42(z0), x1))) A__U72(tt, U51(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatIList(z0), x1)), MARK(U51(isNatIList(z0), x1))) A__U72(tt, U51(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U51(mark(z0), z1), x1)), MARK(U51(U51(z0, z1), x1))) A__U72(tt, U51(U52(z0), x1)) -> c22(A__LENGTH(a__U51(a__U52(mark(z0)), x1)), MARK(U51(U52(z0), x1))) A__U72(tt, U51(isNatList(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNatList(z0), x1)), MARK(U51(isNatList(z0), x1))) A__U72(tt, U51(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U61(mark(z0), z1), x1)), MARK(U51(U61(z0, z1), x1))) A__U72(tt, U51(U62(z0), x1)) -> c22(A__LENGTH(a__U51(a__U62(mark(z0)), x1)), MARK(U51(U62(z0), x1))) A__U72(tt, U51(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U51(a__U71(mark(z0), z1, z2), x1)), MARK(U51(U71(z0, z1, z2), x1))) A__U72(tt, U51(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__U72(mark(z0), z1), x1)), MARK(U51(U72(z0, z1), x1))) A__U72(tt, U51(isNat(z0), x1)) -> c22(A__LENGTH(a__U51(a__isNat(z0), x1)), MARK(U51(isNat(z0), x1))) A__U72(tt, U51(length(z0), x1)) -> c22(A__LENGTH(a__U51(a__length(mark(z0)), x1)), MARK(U51(length(z0), x1))) A__U72(tt, U51(U81(z0), x1)) -> c22(A__LENGTH(a__U51(a__U81(mark(z0)), x1)), MARK(U51(U81(z0), x1))) A__U72(tt, U51(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U51(U91(z0, z1, z2, z3), x1))) A__U72(tt, U51(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U51(U92(z0, z1, z2, z3), x1))) A__U72(tt, U51(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U51(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U51(U93(z0, z1, z2, z3), x1))) A__U72(tt, U51(take(z0, z1), x1)) -> c22(A__LENGTH(a__U51(a__take(mark(z0), mark(z1)), x1)), MARK(U51(take(z0, z1), x1))) A__U72(tt, U51(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U51(cons(mark(z0), z1), x1)), MARK(U51(cons(z0, z1), x1))) A__U72(tt, U51(tt, x1)) -> c22(A__LENGTH(a__U51(tt, x1)), MARK(U51(tt, x1))) A__U72(tt, U51(s(z0), x1)) -> c22(A__LENGTH(a__U51(s(mark(z0)), x1)), MARK(U51(s(z0), x1))) A__U72(tt, U51(x0, z1)) -> c22(MARK(U51(x0, z1))) A__U72(tt, U51(0, x1)) -> c22(A__LENGTH(a__U51(0, x1))) A__U72(tt, U51(nil, x1)) -> c22(A__LENGTH(a__U51(nil, x1))) A__U72(tt, U52(zeros)) -> c22(A__LENGTH(a__U52(a__zeros)), MARK(U52(zeros))) A__U72(tt, U52(U11(z0))) -> c22(A__LENGTH(a__U52(a__U11(mark(z0)))), MARK(U52(U11(z0)))) A__U72(tt, U52(U21(z0))) -> c22(A__LENGTH(a__U52(a__U21(mark(z0)))), MARK(U52(U21(z0)))) A__U72(tt, U52(U31(z0))) -> c22(A__LENGTH(a__U52(a__U31(mark(z0)))), MARK(U52(U31(z0)))) A__U72(tt, U52(U41(z0, z1))) -> c22(A__LENGTH(a__U52(a__U41(mark(z0), z1))), MARK(U52(U41(z0, z1)))) A__U72(tt, U52(U42(z0))) -> c22(A__LENGTH(a__U52(a__U42(mark(z0)))), MARK(U52(U42(z0)))) A__U72(tt, U52(isNatIList(z0))) -> c22(A__LENGTH(a__U52(a__isNatIList(z0))), MARK(U52(isNatIList(z0)))) A__U72(tt, U52(U51(z0, z1))) -> c22(A__LENGTH(a__U52(a__U51(mark(z0), z1))), MARK(U52(U51(z0, z1)))) A__U72(tt, U52(U52(z0))) -> c22(A__LENGTH(a__U52(a__U52(mark(z0)))), MARK(U52(U52(z0)))) A__U72(tt, U52(isNatList(z0))) -> c22(A__LENGTH(a__U52(a__isNatList(z0))), MARK(U52(isNatList(z0)))) A__U72(tt, U52(U61(z0, z1))) -> c22(A__LENGTH(a__U52(a__U61(mark(z0), z1))), MARK(U52(U61(z0, z1)))) A__U72(tt, U52(U62(z0))) -> c22(A__LENGTH(a__U52(a__U62(mark(z0)))), MARK(U52(U62(z0)))) A__U72(tt, U52(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U52(a__U71(mark(z0), z1, z2))), MARK(U52(U71(z0, z1, z2)))) A__U72(tt, U52(U72(z0, z1))) -> c22(A__LENGTH(a__U52(a__U72(mark(z0), z1))), MARK(U52(U72(z0, z1)))) A__U72(tt, U52(isNat(z0))) -> c22(A__LENGTH(a__U52(a__isNat(z0))), MARK(U52(isNat(z0)))) A__U72(tt, U52(length(z0))) -> c22(A__LENGTH(a__U52(a__length(mark(z0)))), MARK(U52(length(z0)))) A__U72(tt, U52(U81(z0))) -> c22(A__LENGTH(a__U52(a__U81(mark(z0)))), MARK(U52(U81(z0)))) A__U72(tt, U52(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U91(mark(z0), z1, z2, z3))), MARK(U52(U91(z0, z1, z2, z3)))) A__U72(tt, U52(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U92(mark(z0), z1, z2, z3))), MARK(U52(U92(z0, z1, z2, z3)))) A__U72(tt, U52(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U52(a__U93(mark(z0), z1, z2, z3))), MARK(U52(U93(z0, z1, z2, z3)))) A__U72(tt, U52(take(z0, z1))) -> c22(A__LENGTH(a__U52(a__take(mark(z0), mark(z1)))), MARK(U52(take(z0, z1)))) A__U72(tt, U52(cons(z0, z1))) -> c22(A__LENGTH(a__U52(cons(mark(z0), z1))), MARK(U52(cons(z0, z1)))) A__U72(tt, U52(0)) -> c22(A__LENGTH(a__U52(0)), MARK(U52(0))) A__U72(tt, U52(tt)) -> c22(A__LENGTH(a__U52(tt)), MARK(U52(tt))) A__U72(tt, U52(s(z0))) -> c22(A__LENGTH(a__U52(s(mark(z0)))), MARK(U52(s(z0)))) A__U72(tt, U52(nil)) -> c22(A__LENGTH(a__U52(nil)), MARK(U52(nil))) A__U72(tt, U52(x0)) -> c22(MARK(U52(x0))) A__U72(tt, isNatList(cons(z0, z1))) -> c22(A__LENGTH(a__U51(a__isNat(z0), z1)), MARK(isNatList(cons(z0, z1)))) A__U72(tt, isNatList(take(z0, z1))) -> c22(A__LENGTH(a__U61(a__isNat(z0), z1)), MARK(isNatList(take(z0, z1)))) A__U72(tt, isNatList(nil)) -> c22(MARK(isNatList(nil))) A__U72(tt, isNatList(z0)) -> c22(MARK(isNatList(z0))) A__U72(tt, U61(zeros, x1)) -> c22(A__LENGTH(a__U61(a__zeros, x1)), MARK(U61(zeros, x1))) A__U72(tt, U61(U11(z0), x1)) -> c22(A__LENGTH(a__U61(a__U11(mark(z0)), x1)), MARK(U61(U11(z0), x1))) A__U72(tt, U61(U21(z0), x1)) -> c22(A__LENGTH(a__U61(a__U21(mark(z0)), x1)), MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(x0)) -> c22(MARK(length(x0))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), 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MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(x0)) -> c22(MARK(length(x0))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (239) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, U81(z0)) -> c22(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) by A__U72(tt, U81(x0)) -> c22(A__LENGTH(U81(mark(x0))), MARK(U81(x0))) A__U72(tt, U81(zeros)) -> c22(A__LENGTH(a__U81(a__zeros)), MARK(U81(zeros))) A__U72(tt, U81(U11(z0))) -> c22(A__LENGTH(a__U81(a__U11(mark(z0)))), MARK(U81(U11(z0)))) A__U72(tt, U81(U21(z0))) -> c22(A__LENGTH(a__U81(a__U21(mark(z0)))), MARK(U81(U21(z0)))) A__U72(tt, U81(U31(z0))) -> c22(A__LENGTH(a__U81(a__U31(mark(z0)))), MARK(U81(U31(z0)))) A__U72(tt, U81(U41(z0, z1))) -> c22(A__LENGTH(a__U81(a__U41(mark(z0), z1))), MARK(U81(U41(z0, z1)))) A__U72(tt, U81(U42(z0))) -> c22(A__LENGTH(a__U81(a__U42(mark(z0)))), MARK(U81(U42(z0)))) A__U72(tt, U81(isNatIList(z0))) -> c22(A__LENGTH(a__U81(a__isNatIList(z0))), MARK(U81(isNatIList(z0)))) A__U72(tt, U81(U51(z0, z1))) -> c22(A__LENGTH(a__U81(a__U51(mark(z0), z1))), MARK(U81(U51(z0, z1)))) A__U72(tt, U81(U52(z0))) -> c22(A__LENGTH(a__U81(a__U52(mark(z0)))), MARK(U81(U52(z0)))) A__U72(tt, U81(isNatList(z0))) -> c22(A__LENGTH(a__U81(a__isNatList(z0))), MARK(U81(isNatList(z0)))) A__U72(tt, U81(U61(z0, z1))) -> c22(A__LENGTH(a__U81(a__U61(mark(z0), z1))), MARK(U81(U61(z0, z1)))) A__U72(tt, U81(U62(z0))) -> c22(A__LENGTH(a__U81(a__U62(mark(z0)))), MARK(U81(U62(z0)))) A__U72(tt, U81(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U81(a__U71(mark(z0), z1, z2))), MARK(U81(U71(z0, z1, z2)))) A__U72(tt, U81(U72(z0, z1))) -> c22(A__LENGTH(a__U81(a__U72(mark(z0), z1))), MARK(U81(U72(z0, z1)))) A__U72(tt, U81(isNat(z0))) -> c22(A__LENGTH(a__U81(a__isNat(z0))), MARK(U81(isNat(z0)))) A__U72(tt, U81(length(z0))) -> c22(A__LENGTH(a__U81(a__length(mark(z0)))), MARK(U81(length(z0)))) A__U72(tt, U81(U81(z0))) -> c22(A__LENGTH(a__U81(a__U81(mark(z0)))), MARK(U81(U81(z0)))) A__U72(tt, U81(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U91(mark(z0), z1, z2, z3))), MARK(U81(U91(z0, z1, z2, z3)))) A__U72(tt, U81(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U92(mark(z0), z1, z2, z3))), MARK(U81(U92(z0, z1, z2, z3)))) A__U72(tt, U81(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U93(mark(z0), z1, z2, z3))), MARK(U81(U93(z0, z1, z2, z3)))) A__U72(tt, U81(take(z0, z1))) -> c22(A__LENGTH(a__U81(a__take(mark(z0), mark(z1)))), MARK(U81(take(z0, z1)))) A__U72(tt, U81(cons(z0, z1))) -> c22(A__LENGTH(a__U81(cons(mark(z0), z1))), MARK(U81(cons(z0, z1)))) A__U72(tt, U81(0)) -> c22(A__LENGTH(a__U81(0)), MARK(U81(0))) A__U72(tt, U81(tt)) -> c22(A__LENGTH(a__U81(tt)), MARK(U81(tt))) A__U72(tt, U81(s(z0))) -> c22(A__LENGTH(a__U81(s(mark(z0)))), MARK(U81(s(z0)))) A__U72(tt, U81(nil)) -> c22(A__LENGTH(a__U81(nil)), MARK(U81(nil))) A__U72(tt, U81(x0)) -> c22(MARK(U81(x0))) ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> c69(A__U93(a__zeros, x1, x2, x3)) MARK(U93(cons(z0, z1), x1, x2, x3)) -> c69(MARK(cons(z0, z1))) MARK(U93(tt, x1, x2, x3)) -> c69(A__U93(tt, x1, x2, x3)) MARK(U93(s(z0), x1, x2, x3)) -> c69(MARK(s(z0))) MARK(take(x0, zeros)) -> c70(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0))) -> c70(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0))) -> c70(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(take(x0, U31(z0))) -> c70(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1))) -> c70(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(take(x0, U42(z0))) -> c70(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c70(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1))) -> c70(A__TAKE(mark(x0), a__U51(mark(z0), z1)), MARK(x0)) MARK(take(x0, U52(z0))) -> c70(A__TAKE(mark(x0), a__U52(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c70(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U61(z0, z1))) -> c70(A__TAKE(mark(x0), a__U61(mark(z0), z1)), MARK(x0)) MARK(take(x0, U62(z0))) -> c70(A__TAKE(mark(x0), a__U62(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1, z2))) -> c70(A__TAKE(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U72(z0, z1))) -> c70(A__TAKE(mark(x0), a__U72(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNat(z0))) -> c70(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, length(z0))) -> c70(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c70(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U92(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U92(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U93(z0, z1, z2, z3))) -> c70(A__TAKE(mark(x0), a__U93(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c70(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c70(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c70(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c70(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c70(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c70(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0), x1)) -> c70(A__TAKE(a__U11(mark(z0)), mark(x1)), MARK(U11(z0))) MARK(take(U21(z0), x1)) -> c70(A__TAKE(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(take(U31(z0), x1)) -> c70(A__TAKE(a__U31(mark(z0)), mark(x1)), MARK(U31(z0))) MARK(take(U41(z0, z1), x1)) -> c70(A__TAKE(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(take(U42(z0), x1)) -> c70(A__TAKE(a__U42(mark(z0)), mark(x1)), MARK(U42(z0))) MARK(take(isNatIList(z0), x1)) -> c70(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1), x1)) -> c70(A__TAKE(a__U51(mark(z0), z1), mark(x1)), MARK(U51(z0, z1))) MARK(take(U52(z0), x1)) -> c70(A__TAKE(a__U52(mark(z0)), mark(x1)), MARK(U52(z0))) MARK(take(isNatList(z0), x1)) -> c70(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U61(z0, z1), x1)) -> c70(A__TAKE(a__U61(mark(z0), z1), mark(x1)), MARK(U61(z0, z1))) MARK(take(U62(z0), x1)) -> c70(A__TAKE(a__U62(mark(z0)), mark(x1)), MARK(U62(z0))) MARK(take(U71(z0, z1, z2), x1)) -> c70(A__TAKE(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(take(U72(z0, z1), x1)) -> c70(A__TAKE(a__U72(mark(z0), z1), mark(x1)), MARK(U72(z0, z1))) MARK(take(isNat(z0), x1)) -> c70(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(length(z0), x1)) -> c70(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c70(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(U92(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U92(mark(z0), z1, z2, z3), mark(x1)), MARK(U92(z0, z1, z2, z3))) MARK(take(U93(z0, z1, z2, z3), x1)) -> c70(A__TAKE(a__U93(mark(z0), z1, z2, z3), mark(x1)), MARK(U93(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c70(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c70(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c70(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c70(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c70(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0))) -> c71(A__TAKE(mark(x0), a__U11(mark(z0))), MARK(U11(z0))) MARK(take(x0, U21(z0))) -> c71(A__TAKE(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(take(x0, U31(z0))) -> c71(A__TAKE(mark(x0), a__U31(mark(z0))), MARK(U31(z0))) MARK(take(x0, U41(z0, z1))) -> c71(A__TAKE(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(take(x0, U42(z0))) -> c71(A__TAKE(mark(x0), a__U42(mark(z0))), MARK(U42(z0))) MARK(take(x0, isNatIList(z0))) -> c71(A__TAKE(mark(x0), a__isNatIList(z0)), 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MARK(U61(U21(z0), x1))) A__U72(tt, U61(U31(z0), x1)) -> c22(A__LENGTH(a__U61(a__U31(mark(z0)), x1)), MARK(U61(U31(z0), x1))) A__U72(tt, U61(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U41(mark(z0), z1), x1)), MARK(U61(U41(z0, z1), x1))) A__U72(tt, U61(U42(z0), x1)) -> c22(A__LENGTH(a__U61(a__U42(mark(z0)), x1)), MARK(U61(U42(z0), x1))) A__U72(tt, U61(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatIList(z0), x1)), MARK(U61(isNatIList(z0), x1))) A__U72(tt, U61(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U51(mark(z0), z1), x1)), MARK(U61(U51(z0, z1), x1))) A__U72(tt, U61(U52(z0), x1)) -> c22(A__LENGTH(a__U61(a__U52(mark(z0)), x1)), MARK(U61(U52(z0), x1))) A__U72(tt, U61(isNatList(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNatList(z0), x1)), MARK(U61(isNatList(z0), x1))) A__U72(tt, U61(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U61(mark(z0), z1), x1)), MARK(U61(U61(z0, z1), x1))) A__U72(tt, U61(U62(z0), x1)) -> c22(A__LENGTH(a__U61(a__U62(mark(z0)), x1)), MARK(U61(U62(z0), x1))) A__U72(tt, U61(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U61(a__U71(mark(z0), z1, z2), x1)), MARK(U61(U71(z0, z1, z2), x1))) A__U72(tt, U61(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__U72(mark(z0), z1), x1)), MARK(U61(U72(z0, z1), x1))) A__U72(tt, U61(isNat(z0), x1)) -> c22(A__LENGTH(a__U61(a__isNat(z0), x1)), MARK(U61(isNat(z0), x1))) A__U72(tt, U61(length(z0), x1)) -> c22(A__LENGTH(a__U61(a__length(mark(z0)), x1)), MARK(U61(length(z0), x1))) A__U72(tt, U61(U81(z0), x1)) -> c22(A__LENGTH(a__U61(a__U81(mark(z0)), x1)), MARK(U61(U81(z0), x1))) A__U72(tt, U61(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U61(U91(z0, z1, z2, z3), x1))) A__U72(tt, U61(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U61(U92(z0, z1, z2, z3), x1))) A__U72(tt, U61(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U61(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U61(U93(z0, z1, z2, z3), x1))) A__U72(tt, U61(take(z0, z1), x1)) -> c22(A__LENGTH(a__U61(a__take(mark(z0), mark(z1)), x1)), MARK(U61(take(z0, z1), x1))) A__U72(tt, U61(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U61(cons(mark(z0), z1), x1)), MARK(U61(cons(z0, z1), x1))) A__U72(tt, U61(tt, x1)) -> c22(A__LENGTH(a__U61(tt, x1)), MARK(U61(tt, x1))) A__U72(tt, U61(s(z0), x1)) -> c22(A__LENGTH(a__U61(s(mark(z0)), x1)), MARK(U61(s(z0), x1))) A__U72(tt, U61(x0, z1)) -> c22(MARK(U61(x0, z1))) A__U72(tt, U61(0, x1)) -> c22(A__LENGTH(a__U61(0, x1))) A__U72(tt, U61(nil, x1)) -> c22(A__LENGTH(a__U61(nil, x1))) A__U72(tt, U62(zeros)) -> c22(A__LENGTH(a__U62(a__zeros)), MARK(U62(zeros))) A__U72(tt, U62(U11(z0))) -> c22(A__LENGTH(a__U62(a__U11(mark(z0)))), MARK(U62(U11(z0)))) A__U72(tt, U62(U21(z0))) -> c22(A__LENGTH(a__U62(a__U21(mark(z0)))), MARK(U62(U21(z0)))) A__U72(tt, U62(U31(z0))) -> c22(A__LENGTH(a__U62(a__U31(mark(z0)))), MARK(U62(U31(z0)))) A__U72(tt, U62(U41(z0, z1))) -> c22(A__LENGTH(a__U62(a__U41(mark(z0), z1))), MARK(U62(U41(z0, z1)))) A__U72(tt, U62(U42(z0))) -> c22(A__LENGTH(a__U62(a__U42(mark(z0)))), MARK(U62(U42(z0)))) A__U72(tt, U62(isNatIList(z0))) -> c22(A__LENGTH(a__U62(a__isNatIList(z0))), MARK(U62(isNatIList(z0)))) A__U72(tt, U62(U51(z0, z1))) -> c22(A__LENGTH(a__U62(a__U51(mark(z0), z1))), MARK(U62(U51(z0, z1)))) A__U72(tt, U62(U52(z0))) -> c22(A__LENGTH(a__U62(a__U52(mark(z0)))), MARK(U62(U52(z0)))) A__U72(tt, U62(isNatList(z0))) -> c22(A__LENGTH(a__U62(a__isNatList(z0))), MARK(U62(isNatList(z0)))) A__U72(tt, U62(U61(z0, z1))) -> c22(A__LENGTH(a__U62(a__U61(mark(z0), z1))), MARK(U62(U61(z0, z1)))) A__U72(tt, U62(U62(z0))) -> c22(A__LENGTH(a__U62(a__U62(mark(z0)))), MARK(U62(U62(z0)))) A__U72(tt, U62(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U62(a__U71(mark(z0), z1, z2))), MARK(U62(U71(z0, z1, z2)))) A__U72(tt, U62(U72(z0, z1))) -> c22(A__LENGTH(a__U62(a__U72(mark(z0), z1))), MARK(U62(U72(z0, z1)))) A__U72(tt, U62(isNat(z0))) -> c22(A__LENGTH(a__U62(a__isNat(z0))), MARK(U62(isNat(z0)))) A__U72(tt, U62(length(z0))) -> c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(x0)) -> c22(MARK(length(x0))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil))) A__U72(tt, U81(x0)) -> c22(A__LENGTH(U81(mark(x0))), MARK(U81(x0))) A__U72(tt, U81(zeros)) -> c22(A__LENGTH(a__U81(a__zeros)), MARK(U81(zeros))) A__U72(tt, U81(U11(z0))) -> c22(A__LENGTH(a__U81(a__U11(mark(z0)))), MARK(U81(U11(z0)))) A__U72(tt, U81(U21(z0))) -> c22(A__LENGTH(a__U81(a__U21(mark(z0)))), MARK(U81(U21(z0)))) A__U72(tt, U81(U31(z0))) -> c22(A__LENGTH(a__U81(a__U31(mark(z0)))), MARK(U81(U31(z0)))) A__U72(tt, U81(U41(z0, z1))) -> c22(A__LENGTH(a__U81(a__U41(mark(z0), z1))), MARK(U81(U41(z0, z1)))) A__U72(tt, U81(U42(z0))) -> c22(A__LENGTH(a__U81(a__U42(mark(z0)))), MARK(U81(U42(z0)))) A__U72(tt, U81(isNatIList(z0))) -> c22(A__LENGTH(a__U81(a__isNatIList(z0))), MARK(U81(isNatIList(z0)))) A__U72(tt, U81(U51(z0, z1))) -> c22(A__LENGTH(a__U81(a__U51(mark(z0), z1))), MARK(U81(U51(z0, z1)))) A__U72(tt, U81(U52(z0))) -> c22(A__LENGTH(a__U81(a__U52(mark(z0)))), MARK(U81(U52(z0)))) A__U72(tt, U81(isNatList(z0))) -> c22(A__LENGTH(a__U81(a__isNatList(z0))), MARK(U81(isNatList(z0)))) A__U72(tt, U81(U61(z0, z1))) -> c22(A__LENGTH(a__U81(a__U61(mark(z0), z1))), MARK(U81(U61(z0, z1)))) A__U72(tt, U81(U62(z0))) -> c22(A__LENGTH(a__U81(a__U62(mark(z0)))), MARK(U81(U62(z0)))) A__U72(tt, U81(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U81(a__U71(mark(z0), z1, z2))), MARK(U81(U71(z0, z1, z2)))) A__U72(tt, U81(U72(z0, z1))) -> c22(A__LENGTH(a__U81(a__U72(mark(z0), z1))), MARK(U81(U72(z0, z1)))) A__U72(tt, U81(isNat(z0))) -> c22(A__LENGTH(a__U81(a__isNat(z0))), MARK(U81(isNat(z0)))) A__U72(tt, U81(length(z0))) -> c22(A__LENGTH(a__U81(a__length(mark(z0)))), MARK(U81(length(z0)))) A__U72(tt, U81(U81(z0))) -> c22(A__LENGTH(a__U81(a__U81(mark(z0)))), MARK(U81(U81(z0)))) A__U72(tt, U81(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U91(mark(z0), z1, z2, z3))), MARK(U81(U91(z0, z1, z2, z3)))) A__U72(tt, U81(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U92(mark(z0), z1, z2, z3))), MARK(U81(U92(z0, z1, z2, z3)))) A__U72(tt, U81(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U93(mark(z0), z1, z2, z3))), MARK(U81(U93(z0, z1, z2, z3)))) A__U72(tt, U81(take(z0, z1))) -> c22(A__LENGTH(a__U81(a__take(mark(z0), mark(z1)))), MARK(U81(take(z0, z1)))) A__U72(tt, U81(cons(z0, z1))) -> c22(A__LENGTH(a__U81(cons(mark(z0), z1))), MARK(U81(cons(z0, z1)))) A__U72(tt, U81(0)) -> c22(A__LENGTH(a__U81(0)), MARK(U81(0))) A__U72(tt, U81(tt)) -> c22(A__LENGTH(a__U81(tt)), MARK(U81(tt))) A__U72(tt, U81(s(z0))) -> c22(A__LENGTH(a__U81(s(mark(z0)))), MARK(U81(s(z0)))) A__U72(tt, U81(nil)) -> c22(A__LENGTH(a__U81(nil)), MARK(U81(nil))) A__U72(tt, U81(x0)) -> c22(MARK(U81(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> 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MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> 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MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), 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c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, 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c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(x0)) -> c22(MARK(length(x0))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil))) A__U72(tt, U81(x0)) -> c22(A__LENGTH(U81(mark(x0))), MARK(U81(x0))) A__U72(tt, U81(zeros)) -> c22(A__LENGTH(a__U81(a__zeros)), MARK(U81(zeros))) A__U72(tt, U81(U11(z0))) -> c22(A__LENGTH(a__U81(a__U11(mark(z0)))), MARK(U81(U11(z0)))) A__U72(tt, U81(U21(z0))) -> c22(A__LENGTH(a__U81(a__U21(mark(z0)))), MARK(U81(U21(z0)))) A__U72(tt, U81(U31(z0))) -> c22(A__LENGTH(a__U81(a__U31(mark(z0)))), MARK(U81(U31(z0)))) A__U72(tt, U81(U41(z0, z1))) -> c22(A__LENGTH(a__U81(a__U41(mark(z0), z1))), MARK(U81(U41(z0, z1)))) A__U72(tt, U81(U42(z0))) -> c22(A__LENGTH(a__U81(a__U42(mark(z0)))), MARK(U81(U42(z0)))) A__U72(tt, U81(isNatIList(z0))) -> c22(A__LENGTH(a__U81(a__isNatIList(z0))), MARK(U81(isNatIList(z0)))) A__U72(tt, U81(U51(z0, z1))) -> c22(A__LENGTH(a__U81(a__U51(mark(z0), z1))), MARK(U81(U51(z0, z1)))) A__U72(tt, U81(U52(z0))) -> c22(A__LENGTH(a__U81(a__U52(mark(z0)))), MARK(U81(U52(z0)))) A__U72(tt, U81(isNatList(z0))) -> c22(A__LENGTH(a__U81(a__isNatList(z0))), MARK(U81(isNatList(z0)))) A__U72(tt, U81(U61(z0, z1))) -> c22(A__LENGTH(a__U81(a__U61(mark(z0), z1))), MARK(U81(U61(z0, z1)))) A__U72(tt, U81(U62(z0))) -> c22(A__LENGTH(a__U81(a__U62(mark(z0)))), MARK(U81(U62(z0)))) A__U72(tt, U81(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U81(a__U71(mark(z0), z1, z2))), MARK(U81(U71(z0, z1, z2)))) A__U72(tt, U81(U72(z0, z1))) -> c22(A__LENGTH(a__U81(a__U72(mark(z0), z1))), MARK(U81(U72(z0, z1)))) A__U72(tt, U81(isNat(z0))) -> c22(A__LENGTH(a__U81(a__isNat(z0))), MARK(U81(isNat(z0)))) A__U72(tt, U81(length(z0))) -> c22(A__LENGTH(a__U81(a__length(mark(z0)))), MARK(U81(length(z0)))) A__U72(tt, U81(U81(z0))) -> c22(A__LENGTH(a__U81(a__U81(mark(z0)))), MARK(U81(U81(z0)))) A__U72(tt, U81(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U91(mark(z0), z1, z2, z3))), MARK(U81(U91(z0, z1, z2, z3)))) A__U72(tt, U81(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U92(mark(z0), z1, z2, z3))), MARK(U81(U92(z0, z1, z2, z3)))) A__U72(tt, U81(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U93(mark(z0), z1, z2, z3))), MARK(U81(U93(z0, z1, z2, z3)))) A__U72(tt, U81(take(z0, z1))) -> c22(A__LENGTH(a__U81(a__take(mark(z0), mark(z1)))), MARK(U81(take(z0, z1)))) A__U72(tt, U81(cons(z0, z1))) -> c22(A__LENGTH(a__U81(cons(mark(z0), z1))), MARK(U81(cons(z0, z1)))) A__U72(tt, U81(0)) -> c22(A__LENGTH(a__U81(0)), MARK(U81(0))) A__U72(tt, U81(tt)) -> c22(A__LENGTH(a__U81(tt)), MARK(U81(tt))) A__U72(tt, U81(s(z0))) -> c22(A__LENGTH(a__U81(s(mark(z0)))), MARK(U81(s(z0)))) A__U72(tt, U81(nil)) -> c22(A__LENGTH(a__U81(nil)), MARK(U81(nil))) A__U72(tt, U81(x0)) -> c22(MARK(U81(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2 ---------------------------------------- (241) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt) -> tt a__U11(z0) -> U11(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt) -> tt a__U31(z0) -> U31(z0) a__U41(tt, z0) -> a__U42(a__isNatIList(z0)) a__U41(z0, z1) -> U41(z0, z1) a__U42(tt) -> tt a__U42(z0) -> U42(z0) a__U51(tt, z0) -> a__U52(a__isNatList(z0)) a__U51(z0, z1) -> U51(z0, z1) a__U52(tt) -> tt a__U52(z0) -> U52(z0) a__U61(tt, z0) -> a__U62(a__isNatIList(z0)) a__U61(z0, z1) -> U61(z0, z1) a__U62(tt) -> tt a__U62(z0) -> U62(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0) -> s(a__length(mark(z0))) a__U72(z0, z1) -> U72(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> a__U92(a__isNat(z1), z0, z1, z2) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__U92(tt, z0, z1, z2) -> a__U93(a__isNat(z2), z0, z1, z2) a__U92(z0, z1, z2, z3) -> U92(z0, z1, z2, z3) a__U93(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U93(z0, z1, z2, z3) -> U93(z0, z1, z2, z3) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatList(z0)) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatList(z0)) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__isNat(z0), z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__isNat(z0), z1) a__isNatList(take(z0, z1)) -> a__U61(a__isNat(z0), z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__isNatList(z1), z1, z0) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__isNatIList(z0)) a__take(s(z0), cons(z1, z2)) -> a__U91(a__isNatIList(z2), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0)) -> a__U11(mark(z0)) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0)) -> a__U31(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U42(z0)) -> a__U42(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1)) -> a__U51(mark(z0), z1) mark(U52(z0)) -> a__U52(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U61(z0, z1)) -> a__U61(mark(z0), z1) mark(U62(z0)) -> a__U62(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1)) -> a__U72(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(U92(z0, z1, z2, z3)) -> a__U92(mark(z0), z1, z2, z3) mark(U93(z0, z1, z2, z3)) -> a__U93(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), 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c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> 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c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> 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c22(A__LENGTH(a__U62(a__length(mark(z0)))), MARK(U62(length(z0)))) A__U72(tt, U62(U81(z0))) -> c22(A__LENGTH(a__U62(a__U81(mark(z0)))), MARK(U62(U81(z0)))) A__U72(tt, U62(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U91(mark(z0), z1, z2, z3))), MARK(U62(U91(z0, z1, z2, z3)))) A__U72(tt, U62(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U92(mark(z0), z1, z2, z3))), MARK(U62(U92(z0, z1, z2, z3)))) A__U72(tt, U62(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U62(a__U93(mark(z0), z1, z2, z3))), MARK(U62(U93(z0, z1, z2, z3)))) A__U72(tt, U62(take(z0, z1))) -> c22(A__LENGTH(a__U62(a__take(mark(z0), mark(z1)))), MARK(U62(take(z0, z1)))) A__U72(tt, U62(cons(z0, z1))) -> c22(A__LENGTH(a__U62(cons(mark(z0), z1))), MARK(U62(cons(z0, z1)))) A__U72(tt, U62(0)) -> c22(A__LENGTH(a__U62(0)), MARK(U62(0))) A__U72(tt, U62(tt)) -> c22(A__LENGTH(a__U62(tt)), MARK(U62(tt))) A__U72(tt, U62(s(z0))) -> c22(A__LENGTH(a__U62(s(mark(z0)))), MARK(U62(s(z0)))) A__U72(tt, U62(nil)) -> c22(A__LENGTH(a__U62(nil)), MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(x0)) -> c22(MARK(length(x0))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil))) A__U72(tt, U81(zeros)) -> c22(A__LENGTH(a__U81(a__zeros)), MARK(U81(zeros))) A__U72(tt, U81(U11(z0))) -> c22(A__LENGTH(a__U81(a__U11(mark(z0)))), MARK(U81(U11(z0)))) A__U72(tt, U81(U21(z0))) -> c22(A__LENGTH(a__U81(a__U21(mark(z0)))), MARK(U81(U21(z0)))) A__U72(tt, U81(U31(z0))) -> c22(A__LENGTH(a__U81(a__U31(mark(z0)))), MARK(U81(U31(z0)))) A__U72(tt, U81(U41(z0, z1))) -> c22(A__LENGTH(a__U81(a__U41(mark(z0), z1))), MARK(U81(U41(z0, z1)))) A__U72(tt, U81(U42(z0))) -> c22(A__LENGTH(a__U81(a__U42(mark(z0)))), MARK(U81(U42(z0)))) A__U72(tt, U81(isNatIList(z0))) -> c22(A__LENGTH(a__U81(a__isNatIList(z0))), MARK(U81(isNatIList(z0)))) A__U72(tt, U81(U51(z0, z1))) -> c22(A__LENGTH(a__U81(a__U51(mark(z0), z1))), MARK(U81(U51(z0, z1)))) A__U72(tt, U81(U52(z0))) -> c22(A__LENGTH(a__U81(a__U52(mark(z0)))), MARK(U81(U52(z0)))) A__U72(tt, U81(isNatList(z0))) -> c22(A__LENGTH(a__U81(a__isNatList(z0))), MARK(U81(isNatList(z0)))) A__U72(tt, U81(U61(z0, z1))) -> c22(A__LENGTH(a__U81(a__U61(mark(z0), z1))), MARK(U81(U61(z0, z1)))) A__U72(tt, U81(U62(z0))) -> c22(A__LENGTH(a__U81(a__U62(mark(z0)))), MARK(U81(U62(z0)))) A__U72(tt, U81(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U81(a__U71(mark(z0), z1, z2))), MARK(U81(U71(z0, z1, z2)))) A__U72(tt, U81(U72(z0, z1))) -> c22(A__LENGTH(a__U81(a__U72(mark(z0), z1))), MARK(U81(U72(z0, z1)))) A__U72(tt, U81(isNat(z0))) -> c22(A__LENGTH(a__U81(a__isNat(z0))), MARK(U81(isNat(z0)))) A__U72(tt, U81(length(z0))) -> c22(A__LENGTH(a__U81(a__length(mark(z0)))), MARK(U81(length(z0)))) A__U72(tt, U81(U81(z0))) -> c22(A__LENGTH(a__U81(a__U81(mark(z0)))), MARK(U81(U81(z0)))) A__U72(tt, U81(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U91(mark(z0), z1, z2, z3))), MARK(U81(U91(z0, z1, z2, z3)))) A__U72(tt, U81(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U92(mark(z0), z1, z2, z3))), MARK(U81(U92(z0, z1, z2, z3)))) A__U72(tt, U81(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U93(mark(z0), z1, z2, z3))), MARK(U81(U93(z0, z1, z2, z3)))) A__U72(tt, U81(take(z0, z1))) -> c22(A__LENGTH(a__U81(a__take(mark(z0), mark(z1)))), MARK(U81(take(z0, z1)))) A__U72(tt, U81(cons(z0, z1))) -> c22(A__LENGTH(a__U81(cons(mark(z0), z1))), MARK(U81(cons(z0, z1)))) A__U72(tt, U81(0)) -> c22(A__LENGTH(a__U81(0)), MARK(U81(0))) A__U72(tt, U81(tt)) -> c22(A__LENGTH(a__U81(tt)), MARK(U81(tt))) A__U72(tt, U81(s(z0))) -> c22(A__LENGTH(a__U81(s(mark(z0)))), MARK(U81(s(z0)))) A__U72(tt, U81(nil)) -> c22(A__LENGTH(a__U81(nil)), MARK(U81(nil))) A__U72(tt, U81(x0)) -> c22(MARK(U81(x0))) S tuples: A__U93(tt, z0, z1, z2) -> c30(MARK(z2)) MARK(isNatIList(z0)) -> c56(A__ISNATILIST(z0)) MARK(isNatList(z0)) -> c59(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c64(A__ISNAT(z0)) MARK(cons(z0, z1)) -> c72(MARK(z0)) MARK(s(z0)) -> c75(MARK(z0)) A__U41(tt, z0) -> c8(A__ISNATILIST(z0)) A__U51(tt, z0) -> c12(A__ISNATLIST(z0)) A__U61(tt, z0) -> c16(A__ISNATILIST(z0)) A__ISNAT(length(z0)) -> c33(A__ISNATLIST(z0)) A__ISNAT(s(z0)) -> c34(A__ISNAT(z0)) A__ISNATILIST(z0) -> c36(A__ISNATLIST(z0)) A__TAKE(0, z0) -> c47(A__ISNATILIST(z0)) MARK(U11(z0)) -> c51(MARK(z0)) MARK(U21(z0)) -> c52(MARK(z0)) MARK(U31(z0)) -> c53(MARK(z0)) MARK(U42(z0)) -> c55(MARK(z0)) MARK(U52(z0)) -> c58(MARK(z0)) MARK(U62(z0)) -> c61(MARK(z0)) MARK(U81(z0)) -> c66(MARK(z0)) A__U71(tt, x0, 0) -> c20(A__U72(tt, x0)) A__U71(tt, x0, z0) -> c20(A__ISNAT(z0)) A__U72(tt, U91(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U72(tt, U92(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) A__U72(tt, U93(z0, z1, z2, z3)) -> c22(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) A__U72(tt, take(z0, z1)) -> c22(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U72(tt, cons(z0, z1)) -> c22(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U72(tt, zeros) -> c22(A__LENGTH(a__zeros)) A__U72(tt, s(z0)) -> c22(MARK(s(z0))) A__U91(tt, x0, length(z0), x2) -> c26(A__U92(a__U11(a__isNatList(z0)), x0, length(z0), x2), A__ISNAT(length(z0))) A__U91(tt, x0, s(z0), x2) -> c26(A__U92(a__U21(a__isNat(z0)), x0, s(z0), x2), A__ISNAT(s(z0))) A__U91(tt, x0, 0, x2) -> c26(A__U92(tt, x0, 0, x2)) A__U91(tt, x0, z0, x2) -> c26(A__ISNAT(z0)) A__U92(tt, x0, x1, length(z0)) -> c28(A__U93(a__U11(a__isNatList(z0)), x0, x1, length(z0)), A__ISNAT(length(z0))) A__U92(tt, x0, x1, s(z0)) -> c28(A__U93(a__U21(a__isNat(z0)), x0, x1, s(z0)), A__ISNAT(s(z0))) A__U92(tt, x0, x1, 0) -> c28(A__U93(tt, x0, x1, 0)) A__U92(tt, x0, x1, z0) -> c28(A__ISNAT(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c38(A__U41(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c38(A__U41(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATILIST(cons(0, x1)) -> c38(A__U41(tt, x1)) A__ISNATILIST(cons(z0, x1)) -> c38(A__ISNAT(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c41(A__U51(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c41(A__U51(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(cons(0, x1)) -> c41(A__U51(tt, x1)) A__ISNATLIST(cons(z0, x1)) -> c41(A__ISNAT(z0)) A__ISNATLIST(take(length(z0), x1)) -> c42(A__U61(a__U11(a__isNatList(z0)), x1), A__ISNAT(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c42(A__U61(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNATLIST(take(0, x1)) -> c42(A__U61(tt, x1)) A__ISNATLIST(take(z0, x1)) -> c42(A__ISNAT(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c45(A__U71(a__U51(a__isNat(z0), z1), cons(z0, z1), x0), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c45(A__U71(a__U61(a__isNat(z0), z1), take(z0, z1), x0), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, nil)) -> c45(A__U71(tt, nil, x0)) A__LENGTH(cons(x0, z0)) -> c45(A__ISNATLIST(z0)) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__U91(a__U31(a__isNatList(z0)), z0, x0, x1), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c48(A__U91(tt, zeros, x0, x1), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c48(A__U91(a__U41(a__isNat(z0), z1), cons(z0, z1), x0, x1), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c48(A__ISNATILIST(z0)) MARK(U41(U11(z0), x1)) -> c54(A__U41(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U41(U21(z0), x1)) -> c54(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0), x1)) -> c54(A__U41(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U41(U41(z0, z1), x1)) -> c54(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U42(z0), x1)) -> c54(A__U41(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U41(U51(z0, z1), x1)) -> c54(A__U41(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U41(U52(z0), x1)) -> c54(A__U41(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U41(U61(z0, z1), x1)) -> c54(A__U41(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U41(U62(z0), x1)) -> c54(A__U41(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c54(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1), x1)) -> c54(A__U41(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U41(length(z0), x1)) -> c54(A__U41(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U41(U81(z0), x1)) -> c54(A__U41(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U41(U92(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U41(U93(z0, z1, z2, z3), x1)) -> c54(A__U41(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1)) -> c54(A__U41(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U41(zeros, x1)) -> c54(A__U41(a__zeros, x1)) MARK(U41(cons(z0, z1), x1)) -> c54(MARK(cons(z0, z1))) MARK(U41(tt, x1)) -> c54(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c54(MARK(s(z0))) MARK(U41(isNatIList(z0), x1)) -> c(A__U41(a__isNatIList(z0), x1)) MARK(U41(isNatIList(z0), x1)) -> c(MARK(isNatIList(z0))) MARK(U41(isNatList(z0), x1)) -> c(A__U41(a__isNatList(z0), x1)) MARK(U41(isNatList(z0), x1)) -> c(MARK(isNatList(z0))) MARK(U41(isNat(z0), x1)) -> c(A__U41(a__isNat(z0), x1)) MARK(U41(isNat(z0), x1)) -> c(MARK(isNat(z0))) MARK(U51(U11(z0), x1)) -> c57(A__U51(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U51(U21(z0), x1)) -> c57(A__U51(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U51(U31(z0), x1)) -> c57(A__U51(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U51(U41(z0, z1), x1)) -> c57(A__U51(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U51(U42(z0), x1)) -> c57(A__U51(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U51(U51(z0, z1), x1)) -> c57(A__U51(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U51(U52(z0), x1)) -> c57(A__U51(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U51(U61(z0, z1), x1)) -> c57(A__U51(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U51(U62(z0), x1)) -> c57(A__U51(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U51(U71(z0, z1, z2), x1)) -> c57(A__U51(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1), x1)) -> c57(A__U51(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U51(length(z0), x1)) -> c57(A__U51(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U51(U81(z0), x1)) -> c57(A__U51(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U51(U92(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U51(U93(z0, z1, z2, z3), x1)) -> c57(A__U51(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1)) -> c57(A__U51(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U51(zeros, x1)) -> c57(A__U51(a__zeros, x1)) MARK(U51(cons(z0, z1), x1)) -> c57(MARK(cons(z0, z1))) MARK(U51(tt, x1)) -> c57(A__U51(tt, x1)) MARK(U51(s(z0), x1)) -> c57(MARK(s(z0))) MARK(U51(isNatIList(z0), x1)) -> c1(A__U51(a__isNatIList(z0), x1)) MARK(U51(isNatIList(z0), x1)) -> c1(MARK(isNatIList(z0))) MARK(U51(isNatList(z0), x1)) -> c1(A__U51(a__isNatList(z0), x1)) MARK(U51(isNatList(z0), x1)) -> c1(MARK(isNatList(z0))) MARK(U51(isNat(z0), x1)) -> c1(A__U51(a__isNat(z0), x1)) MARK(U51(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U61(U11(z0), x1)) -> c60(A__U61(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U61(U21(z0), x1)) -> c60(A__U61(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U61(U31(z0), x1)) -> c60(A__U61(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U61(U41(z0, z1), x1)) -> c60(A__U61(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U61(U42(z0), x1)) -> c60(A__U61(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U61(U51(z0, z1), x1)) -> c60(A__U61(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U61(U52(z0), x1)) -> c60(A__U61(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U61(U61(z0, z1), x1)) -> c60(A__U61(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U61(U62(z0), x1)) -> c60(A__U61(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U61(U71(z0, z1, z2), x1)) -> c60(A__U61(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U61(U72(z0, z1), x1)) -> c60(A__U61(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U61(length(z0), x1)) -> c60(A__U61(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U61(U81(z0), x1)) -> c60(A__U61(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U61(U92(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U61(U93(z0, z1, z2, z3), x1)) -> c60(A__U61(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1)) -> c60(A__U61(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U61(zeros, x1)) -> c60(A__U61(a__zeros, x1)) MARK(U61(cons(z0, z1), x1)) -> c60(MARK(cons(z0, z1))) MARK(U61(tt, x1)) -> c60(A__U61(tt, x1)) MARK(U61(s(z0), x1)) -> c60(MARK(s(z0))) MARK(U61(isNatIList(z0), x1)) -> c2(A__U61(a__isNatIList(z0), x1)) MARK(U61(isNatIList(z0), x1)) -> c2(MARK(isNatIList(z0))) MARK(U61(isNatList(z0), x1)) -> c2(A__U61(a__isNatList(z0), x1)) MARK(U61(isNatList(z0), x1)) -> c2(MARK(isNatList(z0))) MARK(U61(isNat(z0), x1)) -> c2(A__U61(a__isNat(z0), x1)) MARK(U61(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U71(U11(z0), x1, x2)) -> c62(A__U71(a__U11(mark(z0)), x1, x2), MARK(U11(z0))) MARK(U71(U21(z0), x1, x2)) -> c62(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0), x1, x2)) -> c62(A__U71(a__U31(mark(z0)), x1, x2), MARK(U31(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c62(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U42(z0), x1, x2)) -> c62(A__U71(a__U42(mark(z0)), x1, x2), MARK(U42(z0))) MARK(U71(isNatIList(z0), x1, x2)) -> c62(A__U71(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1), x1, x2)) -> c62(A__U71(a__U51(mark(z0), z1), x1, x2), MARK(U51(z0, z1))) MARK(U71(U52(z0), x1, x2)) -> c62(A__U71(a__U52(mark(z0)), x1, x2), MARK(U52(z0))) MARK(U71(isNatList(z0), x1, x2)) -> c62(A__U71(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U71(U61(z0, z1), x1, x2)) -> c62(A__U71(a__U61(mark(z0), z1), x1, x2), MARK(U61(z0, z1))) MARK(U71(U62(z0), x1, x2)) -> c62(A__U71(a__U62(mark(z0)), x1, x2), MARK(U62(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c62(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1), x1, x2)) -> c62(A__U71(a__U72(mark(z0), z1), x1, x2), MARK(U72(z0, z1))) MARK(U71(isNat(z0), x1, x2)) -> c62(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(length(z0), x1, x2)) -> c62(A__U71(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U71(U81(z0), x1, x2)) -> c62(A__U71(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U71(U92(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U92(mark(z0), z1, z2, z3), x1, x2), MARK(U92(z0, z1, z2, z3))) MARK(U71(U93(z0, z1, z2, z3), x1, x2)) -> c62(A__U71(a__U93(mark(z0), z1, z2, z3), x1, x2), MARK(U93(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1, x2)) -> c62(A__U71(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U71(zeros, x1, x2)) -> c62(A__U71(a__zeros, x1, x2)) MARK(U71(cons(z0, z1), x1, x2)) -> c62(MARK(cons(z0, z1))) MARK(U71(tt, x1, x2)) -> c62(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c62(MARK(s(z0))) MARK(U72(U11(z0), x1)) -> c63(A__U72(a__U11(mark(z0)), x1), MARK(U11(z0))) MARK(U72(U21(z0), x1)) -> c63(A__U72(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U72(U31(z0), x1)) -> c63(A__U72(a__U31(mark(z0)), x1), MARK(U31(z0))) MARK(U72(U41(z0, z1), x1)) -> c63(A__U72(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U72(U42(z0), x1)) -> c63(A__U72(a__U42(mark(z0)), x1), MARK(U42(z0))) MARK(U72(isNatIList(z0), x1)) -> c63(A__U72(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U72(U51(z0, z1), x1)) -> c63(A__U72(a__U51(mark(z0), z1), x1), MARK(U51(z0, z1))) MARK(U72(U52(z0), x1)) -> c63(A__U72(a__U52(mark(z0)), x1), MARK(U52(z0))) MARK(U72(isNatList(z0), x1)) -> c63(A__U72(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U72(U61(z0, z1), x1)) -> c63(A__U72(a__U61(mark(z0), z1), x1), MARK(U61(z0, z1))) MARK(U72(U62(z0), x1)) -> c63(A__U72(a__U62(mark(z0)), x1), MARK(U62(z0))) MARK(U72(U71(z0, z1, z2), x1)) -> c63(A__U72(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1), x1)) -> c63(A__U72(a__U72(mark(z0), z1), x1), MARK(U72(z0, z1))) MARK(U72(isNat(z0), x1)) -> c63(A__U72(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U72(length(z0), x1)) -> c63(A__U72(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U72(U81(z0), x1)) -> c63(A__U72(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U72(U91(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U72(U92(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U92(mark(z0), z1, z2, z3), x1), MARK(U92(z0, z1, z2, z3))) MARK(U72(U93(z0, z1, z2, z3), x1)) -> c63(A__U72(a__U93(mark(z0), z1, z2, z3), x1), MARK(U93(z0, z1, z2, z3))) MARK(U72(take(z0, z1), x1)) -> c63(A__U72(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U72(zeros, x1)) -> c63(A__U72(a__zeros, x1)) MARK(U72(cons(z0, z1), x1)) -> c63(MARK(cons(z0, z1))) MARK(U72(tt, x1)) -> c63(A__U72(tt, x1)) MARK(U72(s(z0), x1)) -> c63(MARK(s(z0))) MARK(length(U11(z0))) -> c65(A__LENGTH(a__U11(mark(z0))), MARK(U11(z0))) MARK(length(U21(z0))) -> c65(A__LENGTH(a__U21(mark(z0))), MARK(U21(z0))) MARK(length(U31(z0))) -> c65(A__LENGTH(a__U31(mark(z0))), MARK(U31(z0))) MARK(length(U41(z0, z1))) -> c65(A__LENGTH(a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(length(U42(z0))) -> c65(A__LENGTH(a__U42(mark(z0))), MARK(U42(z0))) MARK(length(isNatIList(z0))) -> c65(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1))) -> c65(A__LENGTH(a__U51(mark(z0), z1)), MARK(U51(z0, z1))) MARK(length(U52(z0))) -> c65(A__LENGTH(a__U52(mark(z0))), MARK(U52(z0))) MARK(length(isNatList(z0))) -> c65(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U61(z0, z1))) -> c65(A__LENGTH(a__U61(mark(z0), z1)), MARK(U61(z0, z1))) MARK(length(U62(z0))) -> c65(A__LENGTH(a__U62(mark(z0))), MARK(U62(z0))) MARK(length(U71(z0, z1, z2))) -> c65(A__LENGTH(a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(length(U72(z0, z1))) -> c65(A__LENGTH(a__U72(mark(z0), z1)), MARK(U72(z0, z1))) MARK(length(isNat(z0))) -> c65(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(length(z0))) -> c65(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c65(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(U92(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U92(mark(z0), z1, z2, z3)), MARK(U92(z0, z1, z2, z3))) MARK(length(U93(z0, z1, z2, z3))) -> c65(A__LENGTH(a__U93(mark(z0), z1, z2, z3)), MARK(U93(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c65(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c65(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c65(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c65(MARK(s(z0))) MARK(U91(U11(z0), x1, x2, x3)) -> c67(A__U91(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U91(U21(z0), x1, x2, x3)) -> c67(A__U91(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U91(U31(z0), x1, x2, x3)) -> c67(A__U91(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U91(U41(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U91(U42(z0), x1, x2, x3)) -> c67(A__U91(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U91(U52(z0), x1, x2, x3)) -> c67(A__U91(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c67(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U61(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U91(U62(z0), x1, x2, x3)) -> c67(A__U91(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U91(U71(z0, z1, z2), x1, x2, x3)) -> c67(A__U91(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U91(U72(z0, z1), x1, x2, x3)) -> c67(A__U91(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U91(isNat(z0), x1, x2, x3)) -> c67(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(length(z0), x1, x2, x3)) -> c67(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c67(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(U92(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U91(U93(z0, z1, z2, z3), x1, x2, x3)) -> c67(A__U91(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c67(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(zeros, x1, x2, x3)) -> c67(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c67(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c67(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c67(MARK(s(z0))) MARK(U92(U11(z0), x1, x2, x3)) -> c68(A__U92(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U92(U21(z0), x1, x2, x3)) -> c68(A__U92(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U92(U31(z0), x1, x2, x3)) -> c68(A__U92(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U92(U41(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U92(U42(z0), x1, x2, x3)) -> c68(A__U92(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U92(isNatIList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U92(U51(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U92(U52(z0), x1, x2, x3)) -> c68(A__U92(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U92(isNatList(z0), x1, x2, x3)) -> c68(A__U92(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U92(U61(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U92(U62(z0), x1, x2, x3)) -> c68(A__U92(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U92(U71(z0, z1, z2), x1, x2, x3)) -> c68(A__U92(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U92(U72(z0, z1), x1, x2, x3)) -> c68(A__U92(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U92(isNat(z0), x1, x2, x3)) -> c68(A__U92(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U92(length(z0), x1, x2, x3)) -> c68(A__U92(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U92(U81(z0), x1, x2, x3)) -> c68(A__U92(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U92(U91(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U92(U92(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U92(U93(z0, z1, z2, z3), x1, x2, x3)) -> c68(A__U92(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U92(take(z0, z1), x1, x2, x3)) -> c68(A__U92(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U92(zeros, x1, x2, x3)) -> c68(A__U92(a__zeros, x1, x2, x3)) MARK(U92(cons(z0, z1), x1, x2, x3)) -> c68(MARK(cons(z0, z1))) MARK(U92(tt, x1, x2, x3)) -> c68(A__U92(tt, x1, x2, x3)) MARK(U92(s(z0), x1, x2, x3)) -> c68(MARK(s(z0))) MARK(U93(U11(z0), x1, x2, x3)) -> c69(A__U93(a__U11(mark(z0)), x1, x2, x3), MARK(U11(z0))) MARK(U93(U21(z0), x1, x2, x3)) -> c69(A__U93(a__U21(mark(z0)), x1, x2, x3), MARK(U21(z0))) MARK(U93(U31(z0), x1, x2, x3)) -> c69(A__U93(a__U31(mark(z0)), x1, x2, x3), MARK(U31(z0))) MARK(U93(U41(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U41(mark(z0), z1), x1, x2, x3), MARK(U41(z0, z1))) MARK(U93(U42(z0), x1, x2, x3)) -> c69(A__U93(a__U42(mark(z0)), x1, x2, x3), MARK(U42(z0))) MARK(U93(isNatIList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U93(U51(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U51(mark(z0), z1), x1, x2, x3), MARK(U51(z0, z1))) MARK(U93(U52(z0), x1, x2, x3)) -> c69(A__U93(a__U52(mark(z0)), x1, x2, x3), MARK(U52(z0))) MARK(U93(isNatList(z0), x1, x2, x3)) -> c69(A__U93(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U93(U61(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U61(mark(z0), z1), x1, x2, x3), MARK(U61(z0, z1))) MARK(U93(U62(z0), x1, x2, x3)) -> c69(A__U93(a__U62(mark(z0)), x1, x2, x3), MARK(U62(z0))) MARK(U93(U71(z0, z1, z2), x1, x2, x3)) -> c69(A__U93(a__U71(mark(z0), z1, z2), x1, x2, x3), MARK(U71(z0, z1, z2))) MARK(U93(U72(z0, z1), x1, x2, x3)) -> c69(A__U93(a__U72(mark(z0), z1), x1, x2, x3), MARK(U72(z0, z1))) MARK(U93(isNat(z0), x1, x2, x3)) -> c69(A__U93(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U93(length(z0), x1, x2, x3)) -> c69(A__U93(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U93(U81(z0), x1, x2, x3)) -> c69(A__U93(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U93(U91(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U93(U92(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U92(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U92(z0, z1, z2, z3))) MARK(U93(U93(z0, z1, z2, z3), x1, x2, x3)) -> c69(A__U93(a__U93(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U93(z0, z1, z2, z3))) MARK(U93(take(z0, z1), x1, x2, x3)) -> c69(A__U93(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U93(zeros, x1, x2, x3)) -> 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MARK(U62(nil))) A__U72(tt, U62(x0)) -> c22(MARK(U62(x0))) A__U72(tt, U71(zeros, x1, x2)) -> c22(A__LENGTH(a__U71(a__zeros, x1, x2)), MARK(U71(zeros, x1, x2))) A__U72(tt, U71(U11(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U11(mark(z0)), x1, x2)), MARK(U71(U11(z0), x1, x2))) A__U72(tt, U71(U21(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U21(mark(z0)), x1, x2)), MARK(U71(U21(z0), x1, x2))) A__U72(tt, U71(U31(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U31(mark(z0)), x1, x2)), MARK(U71(U31(z0), x1, x2))) A__U72(tt, U71(U41(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U41(mark(z0), z1), x1, x2)), MARK(U71(U41(z0, z1), x1, x2))) A__U72(tt, U71(U42(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U42(mark(z0)), x1, x2)), MARK(U71(U42(z0), x1, x2))) A__U72(tt, U71(isNatIList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatIList(z0), x1, x2)), MARK(U71(isNatIList(z0), x1, x2))) A__U72(tt, U71(U51(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U51(mark(z0), z1), x1, x2)), MARK(U71(U51(z0, z1), x1, x2))) A__U72(tt, U71(U52(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U52(mark(z0)), x1, x2)), MARK(U71(U52(z0), x1, x2))) A__U72(tt, U71(isNatList(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNatList(z0), x1, x2)), MARK(U71(isNatList(z0), x1, x2))) A__U72(tt, U71(U61(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U61(mark(z0), z1), x1, x2)), MARK(U71(U61(z0, z1), x1, x2))) A__U72(tt, U71(U62(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U62(mark(z0)), x1, x2)), MARK(U71(U62(z0), x1, x2))) A__U72(tt, U71(U71(z0, z1, z2), x1, x2)) -> c22(A__LENGTH(a__U71(a__U71(mark(z0), z1, z2), x1, x2)), MARK(U71(U71(z0, z1, z2), x1, x2))) A__U72(tt, U71(U72(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__U72(mark(z0), z1), x1, x2)), MARK(U71(U72(z0, z1), x1, x2))) A__U72(tt, U71(isNat(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__isNat(z0), x1, x2)), MARK(U71(isNat(z0), x1, x2))) A__U72(tt, U71(length(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__length(mark(z0)), x1, x2)), MARK(U71(length(z0), x1, x2))) A__U72(tt, U71(U81(z0), x1, x2)) -> c22(A__LENGTH(a__U71(a__U81(mark(z0)), x1, x2)), MARK(U71(U81(z0), x1, x2))) A__U72(tt, U71(U91(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U91(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U91(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U92(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U92(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U92(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(U93(z0, z1, z2, z3), x1, x2)) -> c22(A__LENGTH(a__U71(a__U93(mark(z0), z1, z2, z3), x1, x2)), MARK(U71(U93(z0, z1, z2, z3), x1, x2))) A__U72(tt, U71(take(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(a__take(mark(z0), mark(z1)), x1, x2)), MARK(U71(take(z0, z1), x1, x2))) A__U72(tt, U71(cons(z0, z1), x1, x2)) -> c22(A__LENGTH(a__U71(cons(mark(z0), z1), x1, x2)), MARK(U71(cons(z0, z1), x1, x2))) A__U72(tt, U71(tt, x1, x2)) -> c22(A__LENGTH(a__U71(tt, x1, x2)), MARK(U71(tt, x1, x2))) A__U72(tt, U71(s(z0), x1, x2)) -> c22(A__LENGTH(a__U71(s(mark(z0)), x1, x2)), MARK(U71(s(z0), x1, x2))) A__U72(tt, U71(x0, z1, z2)) -> c22(MARK(U71(x0, z1, z2))) A__U72(tt, U71(0, x1, x2)) -> c22(A__LENGTH(a__U71(0, x1, x2))) A__U72(tt, U71(nil, x1, x2)) -> c22(A__LENGTH(a__U71(nil, x1, x2))) A__U72(tt, U72(zeros, x1)) -> c22(A__LENGTH(a__U72(a__zeros, x1)), MARK(U72(zeros, x1))) A__U72(tt, U72(U11(z0), x1)) -> c22(A__LENGTH(a__U72(a__U11(mark(z0)), x1)), MARK(U72(U11(z0), x1))) A__U72(tt, U72(U21(z0), x1)) -> c22(A__LENGTH(a__U72(a__U21(mark(z0)), x1)), MARK(U72(U21(z0), x1))) A__U72(tt, U72(U31(z0), x1)) -> c22(A__LENGTH(a__U72(a__U31(mark(z0)), x1)), MARK(U72(U31(z0), x1))) A__U72(tt, U72(U41(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U41(mark(z0), z1), x1)), MARK(U72(U41(z0, z1), x1))) A__U72(tt, U72(U42(z0), x1)) -> c22(A__LENGTH(a__U72(a__U42(mark(z0)), x1)), MARK(U72(U42(z0), x1))) A__U72(tt, U72(isNatIList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatIList(z0), x1)), MARK(U72(isNatIList(z0), x1))) A__U72(tt, U72(U51(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U51(mark(z0), z1), x1)), MARK(U72(U51(z0, z1), x1))) A__U72(tt, U72(U52(z0), x1)) -> c22(A__LENGTH(a__U72(a__U52(mark(z0)), x1)), MARK(U72(U52(z0), x1))) A__U72(tt, U72(isNatList(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNatList(z0), x1)), MARK(U72(isNatList(z0), x1))) A__U72(tt, U72(U61(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U61(mark(z0), z1), x1)), MARK(U72(U61(z0, z1), x1))) A__U72(tt, U72(U62(z0), x1)) -> c22(A__LENGTH(a__U72(a__U62(mark(z0)), x1)), MARK(U72(U62(z0), x1))) A__U72(tt, U72(U71(z0, z1, z2), x1)) -> c22(A__LENGTH(a__U72(a__U71(mark(z0), z1, z2), x1)), MARK(U72(U71(z0, z1, z2), x1))) A__U72(tt, U72(U72(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__U72(mark(z0), z1), x1)), MARK(U72(U72(z0, z1), x1))) A__U72(tt, U72(isNat(z0), x1)) -> c22(A__LENGTH(a__U72(a__isNat(z0), x1)), MARK(U72(isNat(z0), x1))) A__U72(tt, U72(length(z0), x1)) -> c22(A__LENGTH(a__U72(a__length(mark(z0)), x1)), MARK(U72(length(z0), x1))) A__U72(tt, U72(U81(z0), x1)) -> c22(A__LENGTH(a__U72(a__U81(mark(z0)), x1)), MARK(U72(U81(z0), x1))) A__U72(tt, U72(U91(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U72(U91(z0, z1, z2, z3), x1))) A__U72(tt, U72(U92(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U92(mark(z0), z1, z2, z3), x1)), MARK(U72(U92(z0, z1, z2, z3), x1))) A__U72(tt, U72(U93(z0, z1, z2, z3), x1)) -> c22(A__LENGTH(a__U72(a__U93(mark(z0), z1, z2, z3), x1)), MARK(U72(U93(z0, z1, z2, z3), x1))) A__U72(tt, U72(take(z0, z1), x1)) -> c22(A__LENGTH(a__U72(a__take(mark(z0), mark(z1)), x1)), MARK(U72(take(z0, z1), x1))) A__U72(tt, U72(cons(z0, z1), x1)) -> c22(A__LENGTH(a__U72(cons(mark(z0), z1), x1)), MARK(U72(cons(z0, z1), x1))) A__U72(tt, U72(tt, x1)) -> c22(A__LENGTH(a__U72(tt, x1)), MARK(U72(tt, x1))) A__U72(tt, U72(s(z0), x1)) -> c22(A__LENGTH(a__U72(s(mark(z0)), x1)), MARK(U72(s(z0), x1))) A__U72(tt, U72(x0, z1)) -> c22(MARK(U72(x0, z1))) A__U72(tt, U72(0, x1)) -> c22(A__LENGTH(a__U72(0, x1))) A__U72(tt, U72(nil, x1)) -> c22(A__LENGTH(a__U72(nil, x1))) A__U72(tt, isNat(length(z0))) -> c22(A__LENGTH(a__U11(a__isNatList(z0))), MARK(isNat(length(z0)))) A__U72(tt, isNat(s(z0))) -> c22(A__LENGTH(a__U21(a__isNat(z0))), MARK(isNat(s(z0)))) A__U72(tt, isNat(0)) -> c22(MARK(isNat(0))) A__U72(tt, isNat(z0)) -> c22(MARK(isNat(z0))) A__U72(tt, length(zeros)) -> c22(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U72(tt, length(U11(z0))) -> c22(A__LENGTH(a__length(a__U11(mark(z0)))), MARK(length(U11(z0)))) A__U72(tt, length(U21(z0))) -> c22(A__LENGTH(a__length(a__U21(mark(z0)))), MARK(length(U21(z0)))) A__U72(tt, length(U31(z0))) -> c22(A__LENGTH(a__length(a__U31(mark(z0)))), MARK(length(U31(z0)))) A__U72(tt, length(U41(z0, z1))) -> c22(A__LENGTH(a__length(a__U41(mark(z0), z1))), MARK(length(U41(z0, z1)))) A__U72(tt, length(U42(z0))) -> c22(A__LENGTH(a__length(a__U42(mark(z0)))), MARK(length(U42(z0)))) A__U72(tt, length(isNatIList(z0))) -> c22(A__LENGTH(a__length(a__isNatIList(z0))), MARK(length(isNatIList(z0)))) A__U72(tt, length(U51(z0, z1))) -> c22(A__LENGTH(a__length(a__U51(mark(z0), z1))), MARK(length(U51(z0, z1)))) A__U72(tt, length(U52(z0))) -> c22(A__LENGTH(a__length(a__U52(mark(z0)))), MARK(length(U52(z0)))) A__U72(tt, length(isNatList(z0))) -> c22(A__LENGTH(a__length(a__isNatList(z0))), MARK(length(isNatList(z0)))) A__U72(tt, length(U61(z0, z1))) -> c22(A__LENGTH(a__length(a__U61(mark(z0), z1))), MARK(length(U61(z0, z1)))) A__U72(tt, length(U62(z0))) -> c22(A__LENGTH(a__length(a__U62(mark(z0)))), MARK(length(U62(z0)))) A__U72(tt, length(U71(z0, z1, z2))) -> c22(A__LENGTH(a__length(a__U71(mark(z0), z1, z2))), MARK(length(U71(z0, z1, z2)))) A__U72(tt, length(U72(z0, z1))) -> c22(A__LENGTH(a__length(a__U72(mark(z0), z1))), MARK(length(U72(z0, z1)))) A__U72(tt, length(isNat(z0))) -> c22(A__LENGTH(a__length(a__isNat(z0))), MARK(length(isNat(z0)))) A__U72(tt, length(length(z0))) -> c22(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U72(tt, length(U81(z0))) -> c22(A__LENGTH(a__length(a__U81(mark(z0)))), MARK(length(U81(z0)))) A__U72(tt, length(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U91(mark(z0), z1, z2, z3))), MARK(length(U91(z0, z1, z2, z3)))) A__U72(tt, length(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U92(mark(z0), z1, z2, z3))), MARK(length(U92(z0, z1, z2, z3)))) A__U72(tt, length(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__length(a__U93(mark(z0), z1, z2, z3))), MARK(length(U93(z0, z1, z2, z3)))) A__U72(tt, length(take(z0, z1))) -> c22(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U72(tt, length(cons(z0, z1))) -> c22(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U72(tt, length(s(z0))) -> c22(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U72(tt, length(x0)) -> c22(MARK(length(x0))) A__U72(tt, length(0)) -> c22(A__LENGTH(a__length(0))) A__U72(tt, length(tt)) -> c22(A__LENGTH(a__length(tt))) A__U72(tt, length(nil)) -> c22(A__LENGTH(a__length(nil))) A__U72(tt, U81(zeros)) -> c22(A__LENGTH(a__U81(a__zeros)), MARK(U81(zeros))) A__U72(tt, U81(U11(z0))) -> c22(A__LENGTH(a__U81(a__U11(mark(z0)))), MARK(U81(U11(z0)))) A__U72(tt, U81(U21(z0))) -> c22(A__LENGTH(a__U81(a__U21(mark(z0)))), MARK(U81(U21(z0)))) A__U72(tt, U81(U31(z0))) -> c22(A__LENGTH(a__U81(a__U31(mark(z0)))), MARK(U81(U31(z0)))) A__U72(tt, U81(U41(z0, z1))) -> c22(A__LENGTH(a__U81(a__U41(mark(z0), z1))), MARK(U81(U41(z0, z1)))) A__U72(tt, U81(U42(z0))) -> c22(A__LENGTH(a__U81(a__U42(mark(z0)))), MARK(U81(U42(z0)))) A__U72(tt, U81(isNatIList(z0))) -> c22(A__LENGTH(a__U81(a__isNatIList(z0))), MARK(U81(isNatIList(z0)))) A__U72(tt, U81(U51(z0, z1))) -> c22(A__LENGTH(a__U81(a__U51(mark(z0), z1))), MARK(U81(U51(z0, z1)))) A__U72(tt, U81(U52(z0))) -> c22(A__LENGTH(a__U81(a__U52(mark(z0)))), MARK(U81(U52(z0)))) A__U72(tt, U81(isNatList(z0))) -> c22(A__LENGTH(a__U81(a__isNatList(z0))), MARK(U81(isNatList(z0)))) A__U72(tt, U81(U61(z0, z1))) -> c22(A__LENGTH(a__U81(a__U61(mark(z0), z1))), MARK(U81(U61(z0, z1)))) A__U72(tt, U81(U62(z0))) -> c22(A__LENGTH(a__U81(a__U62(mark(z0)))), MARK(U81(U62(z0)))) A__U72(tt, U81(U71(z0, z1, z2))) -> c22(A__LENGTH(a__U81(a__U71(mark(z0), z1, z2))), MARK(U81(U71(z0, z1, z2)))) A__U72(tt, U81(U72(z0, z1))) -> c22(A__LENGTH(a__U81(a__U72(mark(z0), z1))), MARK(U81(U72(z0, z1)))) A__U72(tt, U81(isNat(z0))) -> c22(A__LENGTH(a__U81(a__isNat(z0))), MARK(U81(isNat(z0)))) A__U72(tt, U81(length(z0))) -> c22(A__LENGTH(a__U81(a__length(mark(z0)))), MARK(U81(length(z0)))) A__U72(tt, U81(U81(z0))) -> c22(A__LENGTH(a__U81(a__U81(mark(z0)))), MARK(U81(U81(z0)))) A__U72(tt, U81(U91(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U91(mark(z0), z1, z2, z3))), MARK(U81(U91(z0, z1, z2, z3)))) A__U72(tt, U81(U92(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U92(mark(z0), z1, z2, z3))), MARK(U81(U92(z0, z1, z2, z3)))) A__U72(tt, U81(U93(z0, z1, z2, z3))) -> c22(A__LENGTH(a__U81(a__U93(mark(z0), z1, z2, z3))), MARK(U81(U93(z0, z1, z2, z3)))) A__U72(tt, U81(take(z0, z1))) -> c22(A__LENGTH(a__U81(a__take(mark(z0), mark(z1)))), MARK(U81(take(z0, z1)))) A__U72(tt, U81(cons(z0, z1))) -> c22(A__LENGTH(a__U81(cons(mark(z0), z1))), MARK(U81(cons(z0, z1)))) A__U72(tt, U81(0)) -> c22(A__LENGTH(a__U81(0)), MARK(U81(0))) A__U72(tt, U81(tt)) -> c22(A__LENGTH(a__U81(tt)), MARK(U81(tt))) A__U72(tt, U81(s(z0))) -> c22(A__LENGTH(a__U81(s(mark(z0)))), MARK(U81(s(z0)))) A__U72(tt, U81(nil)) -> c22(A__LENGTH(a__U81(nil)), MARK(U81(nil))) A__U72(tt, U81(x0)) -> c22(MARK(U81(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_1, a__U21_1, a__U31_1, a__U41_2, a__U42_1, a__U51_2, a__U52_1, a__U61_2, a__U62_1, a__U71_3, a__U72_2, a__U81_1, a__U91_4, a__U92_4, a__U93_4, a__isNat_1, a__isNatIList_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U93_4, MARK_1, A__U41_2, A__U51_2, A__U61_2, A__ISNAT_1, A__ISNATILIST_1, A__TAKE_2, A__U71_3, A__U72_2, A__U91_4, A__U92_4, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c30_1, c56_1, c59_1, c64_1, c72_1, c75_1, c8_1, c12_1, c16_1, c33_1, c34_1, c36_1, c47_1, c51_1, c52_1, c53_1, c55_1, c58_1, c61_1, c66_1, c20_1, c22_2, c22_1, c26_2, c26_1, c28_2, c28_1, c38_2, c38_1, c41_2, c41_1, c42_2, c42_1, c45_2, c45_1, c48_2, c48_1, c54_2, c54_1, c_1, c57_2, c57_1, c1_1, c60_2, c60_1, c2_1, c62_2, c62_1, c63_2, c63_1, c65_2, c65_1, c67_2, c67_1, c68_2, c68_1, c69_2, c69_1, c70_2, c70_1, c71_2, c71_1, c20_2